Yu Yan make a wall hanging from a piece of fabric. For the firt part, he cut off 1/3 of the length of the original piece of fabric. For the next two part, he cut off 10 inche and 5 inche from the length of the remaining fabric. In total, he cut 35 1/2 inche from the length of the original piece of fabric. How long wa the original piece of fabric? Write and olve an equation. Check your olution. ​

Based on the constructed difference table, the next term of this sequence 6, −2, −3, 7, 32, 76, . . . is 143.

In Mathematics, a sequence can be defined as a series of real and natural numbers in which each term or list of elements are ordered in a particular order and repetitions are allowed.

In Mathematics, a difference table can be defined as a type of table that is constructed by subtracting adjacent elements (entries) in a sequence, and then repeating the process with next those elements (entries).

Number            Difference from previous             Difference of differences

6

-2                               -8                                          

-3                               -1                                                7            

7                                 10                                              11            4

32                               25                                             15            4

76                              44                                               19            4

143                            67                                                23           4

First column: -2 - 6 = -8; -3 - (-2) = 1; ....... 143 - 76 = 67.

Second column: -1 - (-8) = 7; 10 - (-1) = 11; .... 67 - 44 = 23.

Third column: 11 - 7 = 4; 15 - 11 = 4 .... 23 - 19 = 4.

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The maximum value of log(x)/ x is 1/e.

The function given is f(x) = log(x)/ x

As base is not mentioned assuming that the base is e.

To find maximum value, let us find the critical point of this function equating its first derivative to 0.

d/dx (f(x) = log(x)/ x) = ( 1 - log(x))/ x²

So d/dx (f(x)) = 0 when 1 - log(x) = 0

That is log(x) = 1

So x = e

f''(x) = (2log(x) - 3)/ x³

f''(e) = (2log(e) - 3)/ e³ = -1/e³ < 0

So at x = e, f(x) is maximum.

Thus maximum value of f(x) is at x = e

f(e) = log(e)/ e = 1/e

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To see the Polar form and Rectangular form of quotient as a complex number.

Polar numbers can be written in two different forms: rectangular and polar. Rectangular complex numbers are given by a + bi, where a represents the real part of the complex number and b represents the imaginary part of the complex number. Polar complex numbers are given by its absolute value,

r = [tex]\sqrt{x^{2} +y^2}[/tex] and the argument, θ, which can then be determined through the following relations:

[tex]z=re^i^\theta[/tex]

If the complex numbers are in polar form, then the quotient is given by:

[tex]\frac{z_1}{z_2}=\frac{r_1e^i^\theta_1}{r_2e^i^\theta_2}[/tex]  [tex]= \frac{r_1}{r_2}e^i^(^\theta_1^-^\theta_2^)[/tex]

If the complex numbers are in rectangular form, then you will have to use the complex conjugate to remove the complex number in the denominator:

[tex]\frac{a_1+b_1i}{a_2+b_2i}[/tex] [tex]=\frac{(a_1+b_1i)(a_2-b_2i)}{(a_2+b_2i)(a_2-b_2i)}[/tex].

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The process of solving systems by elimination with multiplication for the equation is explained below.

In math the term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign.

Here we need to write down the steps to solve systems by elimination with multiplication.

Here the first steps id to out the equations in Standard Form.

And then here we need to determine which variable to eliminate.

Finally we have to Multiply the equations and solve.

And this process that allows us to multiply both sides of an equation by the same constant while still having an equivalent expression.

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A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.

A parabola is formed by cutting a right circular cone in half along a plane perpendicular to the cone's generator. It is a locus of a moving point whose separation from the focus is equal to its separation from a stationary line (directrix)

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Answer: 1) 1,500     2) 36     3) 15     4) 8,400

Step-by-step explanation: Hope it helps!

Therefore, if the borrower had paid the loan just at the end of the second year, he would have owed R 167250. The additional interest due would be R 167250 - 150000 = R 17250.

a) To calculate the amount of money that the person would have to pay at the end of the second year to clear his debt, you can use the formula for compound interest:l,

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the person took a loan of R 150000 for 2 years at an annual interest rate of 10%. He paid R 85000 at the end of the first year. So, the new principal at the beginning of the second year is P = 150000 - 85000 = 65000.

So, A = P(1 + r/n)^(nt)

A = 65000(1 + 0.1)^2

A = 65000*1.1^2

A = 73,650

So, the person should have to pay R 73650 at the end of the second year to clear his debt.

b) If the person had paid the loan only at the end of the second year, the interest would have been calculated on the original principal of R 150000 for 2 years. So,

A = P(1 + r/n)^(nt)

A = 150000(1 + 0.1)^2

A = 150000*1.1^2

A = 167250

So, the person would have had to pay R 167250 if he had paid the loan only at the end of the second year. Therefore, he would have to pay more interest of R 167250 - 150000 = R 17250.

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To calculate the volume of a triangular prism, you need to know the base area and the height. In this case, the base area is given as 4 cm^2, and the areas of the sides are given as 9 cm^2, 10 cm^2 and 17 cm^2.

To find the volume of the prism, you can use the formula:

Volume = Base Area x Height

Since we don't know the height of the prism, we can use the area of the sides to find the height.

To find the height, we need to use the formula of area of the triangle.

Area = (1/2) x b x h

let's use the area of one side (for example 9cm^2)

9cm^2 = (1/2) x b x h

we can divide both sides by (1/2) x b

h = (2 * 9cm^2) / b

Now we have the height of the triangular prism, so we can use that to find the volume.

so the volume of the triangular prism = Base Area x Height = 4cm^2 x ( (2 * 9cm^2) / b) = 72/b cm^3

As we don't know the value of b, we can't find the exact volume of the prism.

Answer:

12 cm³

Step-by-step explanation:

Conditions:
a * h = 9 cm
b * h = 10 cm
c * h = 17 cm
S = 4 cm²

To calculate the area on three sides, we use the Heron formula:

[tex]S = \sqrt{p * (p-a) *(p-b)*(p-c)[/tex]
where "p" is the semi-perimeter:
[tex]p = \frac{(a+b+c)}{2}[/tex]

Let's express the sides in terms of the height:
a = 9/h
b = 10/h
c = 17/h

Then the semiperimeter will be:
p = (9/h+10/h+17/h) : 2 = 36/h : 2 = 18/h

Substituting the values into the Heron formula:
4 = √(18/h * (18/h - 9/h) * (18/h - 10/h) * (18/h - 17/h))
4² = 18/h * (18/h - 9/h) * (18/h - 10/h) * (18/h - 17/h)
16 = 18/h * 9/h * 8/h * 1/h
16 = 1296 / h^4
h^4 = 1296 / 16 = 81
h = 3 cm

Now we can calculate the volume of the pyramid:
V = S * h = 4 cm² * 3 cm = 12 cm³

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The cosine function (also known as the cos function) in triangles is the ratio between the neighbouring side and the hypotenuse.

The complement of sine and one of the three primary trigonometric functions, cosine is one of the three basic trigonometric functions.

The cosine of a right triangle is the ratio between the lengths of the adjacent side and the longest side, or hypotenuse.

Adjacent Side/Hypotenuse = cos theta

If the ratio between the side and hypotenuse is known, the cos inverse function can be used to calculate the angle of any right-angled triangle. The symbol for the cos inverse is [tex]cosx^{-1}[/tex].

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The cosine function (also known as the cos function) in triangles is the ratio between the neighbouring side and the hypotenuse.

The complement of sine and one of the three primary trigonometric functions, cosine is one of the three basic trigonometric functions.

The cosine of a right triangle is the ratio between the lengths of the adjacent side and the longest side, or hypotenuse.

Adjacent Side/Hypotenuse = cos theta

If the ratio between the side and hypotenuse is known, the cos inverse function can be used to calculate the angle of any right-angled triangle. The symbol for the cos inverse is .

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An expression of more than two algebraic terms is called Polynomial.

Polynomials are made up of two terms: poly (meaning "many") and nominal (meaning "terms"). A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division (not division by a variable). Based on the number of terms in the expression, it is classified as monomial, binomial, and ternary. Examples of constants, variables, and exponents are:

Polynomials can be classified by degree and power. Based on the number of terms, there are three main types of polynomials:

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Answer:

You start your first timer, and let it run out, then either let the second timer run for 2 minutes, then take the eggs out.

Step-by-step explanation:

Answer: The prime factorization of 630 is 2 x 3 x 5 x 7.

The prime factorization of 1248 is 2^4 x 3 x 7.

So, 630 can be written as 2 x 3 x 5 x 7 and 1248 can be written as 2^4 x 3 x 7

In general, to find the prime factorization of a number, you can divide the number by the smallest prime number (2) and continue dividing by prime numbers until the quotient is a prime number. Then divide that quotient by the next smallest prime number, and so on, until the quotient is 1.

Step-by-step explanation:

The y-intercept of the equation y = -4x-6 is (0, -6).

Equation: y = -4x - 6

The y intercept of a graph is the point where the graph intersects the y-axis. We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is

y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Find the values of m and b, using the slope-intercept equation.

Now, using this information,

y = −4x − 6

y = mx + c

m → slope

the slope is −4 and

y−intercept would be (0,−6).

Thus, the y-intercept is (0, -6).

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This equation can be solved using the addition and subtraction property of equality, x + 7 = 13.

An equation is an expression containing an equal sign that states the equality of two mathematical expressions. It is a statement that two expressions have the same value. Equations often involve variables, which are placeholders for unknown numbers. An equation contains at least one operation, such as addition, subtraction, multiplication, or division. Equations are used in a variety of mathematical applications, from basic algebra to more advanced topics such as calculus.

Subtract 7 from both sides to isolate x.

x + 7 - 7 = 13 - 7

x = 6

Therefore, the two step equation that equals 13 is x + 7 = 13.

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The scale factor used in the scale drawing which has the scale of 6 centimeters = 7 meters is 116.667

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

For the scale drawing with a scale of scale of 6 centimeters = 7 meters

the units are converted to be same, using the conversion unit of

100 cm = 1 m

x cm  = 7 meters'

solving for x

x = 700 cm

hence the scale of the drawing is 6 cm = 700 cm, we solve for the scale factor

6 cm = 700 cm

1 cm = scale factor

solving for the scale factor

scale factor = 700 / 6

= 350 / 3

the factor is 116.667

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Answer: The option that is NOT a possible way to evaluate the function and find the correct answer is

See what x is when y=-5

Explanation:

In the function f(x) = 3x^2 - 2x + 5, x is the input variable and y is the output variable. To find the value of f(-5), we need to substitute -5 wherever there is an x in the function and then solve the resulting expression. This is the first option.

The second and forth options are also correct ways to evaluate the function, they involve graphing the equation and finding the y-value of the ordered pair when x=-5.

But the third option is not the correct way, because it is asking to find x when y=-5, but in the given function the y is unknown, so it is not possible to find x when y=-5.

Step-by-step explanation:

The equation of a sphere if one of its diameters has endpoint (2, 1, 4) and (4, 3, 10) is (x+1)²+(y-1)²+(z+3)²= 11

Using the distance equation to find the distance of the diameter:

d² = (xf-xi)² + (yf-yi)² +(zf-zi)²

d² = (2-4)²+(1-3)²+(4-10)²

d²=4+4+36=44

d=sqrt(44)

The radius is half the diameter,  which is: r=d/2

r=sqrt(44)/2

To find the middle of the diameter we are using the center equation:

(xf-xi)/2, (yf-yi)/2, (zf-zi)/2

(2-4)/2, (1-3)/2, (4-10)/2

(-1,1,-3) Center

Now, using the equation for a sphere:

(x-xc)²+(y-yc)²+(z-zc)²=r²

(x+1)²+(y-1)²+(z+3)²=(sqrt(44)/2)²

(x+1)²+(y-1)²+(z+3)²=44/4

(x+1)²+(y-1)²+(z+3)²= 11

Thus, the equation of a sphere if one of its diameters has endpoint (2, 1, 4) and (4, 3, 10) is (x+1)²+(y-1)²+(z+3)²= 11

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d² = (xf-xi)² + (yf-yi)² +(zf-zi)²

d² = (2-4)²+(1-3)²+(4-10)²

d²=4+4+36=44

d=sqrt(44)

The radius is half the diameter,  which is: r=d/2

r=sqrt(44)/2

(xf-xi)/2, (yf-yi)/2, (zf-zi)/2

(2-4)/2, (1-3)/2, (4-10)/2

(-1,1,-3) Center

Yes. 144 is a perfect square. It is a perfect square of 12. The integer that can be expressed as the square of another integer is called as a perfect square.

A number is said to be a perfect square if its square root is an integer. It  means that a perfect square is an integer's product with itself. It is also defined as the second exponent of an integer. A number squaring a whole number is a perfect square. A perfect square can be determined by the prime factorization method. Prime factorization is defined as the  process of writing all numbers as a product of prime. Through prime factorization we can determine the square root. Every integer has its prime factorization.

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The vertex of the graph of  y = 3x² + 2x + 1 is (-0.33, 1.33)

We know that the general form of a parabola is given by an equation y = ax² + bx + c.

the x coordinate of the vertex of the quadratic equation is given by the formula -b/(2a)

To find y-coordinate we substitute value of x in given quadratic equation and solve it for x.

Consider given quadratic equation y = 3x² + 2x + 1

Comparing given quadratic equation y = 3x² + 2x + 1 with y = ax² + bx + c we get, a = 3, b = 2 and c = 1

The x-coordinate of vertex would be,

-b/(2a)

= -2/(2 × 3)

= -2/6

= -1/3

= - 0.33

substitute x = -1/3 in given quadrtic equation in order to find the y-coordinate.

 y = 3(-1/3)² + 2(-1/3) + 1

y = (-1)² - 2/3 + 1

y = 2 - 2/3

y = 4/3

y = 1.33

So, (-1/3, 4/3) is the vertex.

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The average expenditure which I did by the maximum number of the manual worker is 1847.826

We note that the maximum frequency for the class 1500–2000 is 40. As a result, it belongs to the modal class.

The class interval with the most data points, or what we may refer to as the highest frequency, inside a collection of data is called the modal class.

The class that will include the mode is known as the modal class. The modal class may be determined using the formula I0 I 0 + (f1−f02f1−f0−f2)h ( f 1 − f 0 2 f 1 − f 0 − f 2 ) h

l=1500,h=500,f=40,f

1=24, and f 2=33

∴Mode=(l+ 2f−f1/2f−f2f−f 1 )×h

Mode=1500+ 40−24 / 80−24−33×500

⇒Mode=1500+ 16/23 ×500

=1847.826

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Answer:

Step-by-step explanation:

y= 1/4x + 2.5

Answer:

QP = 2

QR = 2√3

Step-by-step explanation:

This is a special right triangle with angle measures as follows:

30° - 60° - 90°

And side lengths represented with:

x - x√3 - 2x respectively to angle measures.

The side length that sees angle measure 90, hypotenuse, is given as 4 so the legs would be:

2 and 2√3

A 360-degree angle can be visualized as a full rotation or circle, and it is often used to measure angles in a circular context.

A 360-degree angle is a complete rotation and is equivalent to one full circle. It is often represented as a circle with a line that goes from the center of the circle to the outer edge, marking the angle.

When looking at a 360-degree angle, it can be divided into four quadrants: the top right, top left, bottom left, and bottom right. Each quadrant is 90 degrees or one-fourth of the total angle. This division is useful when analyzing or measuring angles in different sections of a circle.

In terms of visual representation, imagine a clock face with the numbers 1-12. The clock face is a 360-degree angle, with each number representing a 30 degree increment. The hour hand of the clock would rotate around the face, completing a full rotation and reaching the starting point at the 12 o'clock position, completing a 360 degree angle.

In other words, a 360 degree angle can be visualized as a full rotation or circle, and it is often used to measure angles in a circular context. It can also be divided into smaller sections for analysis or measurement purposes.

Therefore, A 360 degree angle can be visualized as a full rotation or circle, and it is often used to measure angles in a circular context.

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The reduced row-echelon form of the augmented matrix for the system of equations is: 1 0 0 1 | 8, 0 1 0 -2 | -2, 0 0 1 0 | 0. This means that the first equation is reduced to x_1 + x_4 = 8, the second equation is reduced to x_2 - 2x_4 = -2, and the third equation is reduced to x_3 = 0.

Step 1: Subtract 2 times row 1 from row 2 to get row 2 in the form [0 1 0 -2 | -2].

Step 2: Divide row 2 by -2 to get row 2 in the form [0 1 0 1 | 8].

Step 3: Subtract 3 times row 2 from row 1 to get row 1 in the form [1 0 0 1 | 8].

Step 4: Subtract 4 times row 2 from row 3 to get row 3 in the form [0 0 1 0 | 0].

Step 5: The reduced row-echelon form of the augmented matrix for the system of equations is now: [1 0 0 1 | 8], [0 1 0 -2 | -2], [0 0 1 0 | 0]. This means that the first equation is reduced to x_1 + x_4 = 8, the second equation is reduced to x_2 - 2x_4 = -2, and the third equation is reduced to x_3 = 0.

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The zeros of function p(x) = 5 - x² are x = √5 and x = -√5

Consider given polynomial function.

p(x) = 5 - x²

We know that the zeros of a function are the values of the variable of the function that makes the function value equal to 0.

To find the zeros of function p(x), we need to equate p(x) to zero then solve it for x.

⇒ p(x) = 0

⇒ 5 - x² = 0

⇒ 5 - x² - 5 = 0 - 5          ....(subtract 5 from each side of equation)

⇒ -x² = -5

⇒ x² = 5                            ......(multiply both the sides by -1)

⇒ x = ±√5                         .........(taking square-root of both the sides)

Thus x = √5 and x = -√5 are zeros.              

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The complete question is:

What are the zeros of p(x) = 5 - x²?.

As a result, there is just one transformation from shape A to shape B: dilate A by 1/2, followed by a 180 degree rotation.

A drastic change in shape or appearance is called a transformation. An crucial occasion, such as receiving your driver's licence, enrolling in college, or getting married, might change the course of your life. Extreme, dramatic change is what we refer to as transformation.

When we move a figure in any direction, we say that we are translating. Flipping a figure over a line is what is meant by reflection. Rotation is the process of rotating a figure around a point by a specific amount. When we dilate a figure, it is enlarged or shrunk.

By multiplying the original shape by a scale factor, we can change the size of the shape and make it bigger or smaller. This type of modification is called an expansion.

A shape can be transformed by shifting its location and size.

Shape A can only be transformed into shape B by rotating 180 degrees and enlarging it by half.

Based on the figure, we can:

Shape A's side lengths are twice as long as Shape B's side lengths.

After dilatation, shape A can be rotated 180 degrees to imprint onto shape B.

The range of dilatation from shape A to shape B is thus:

Scale = 1/2

As a result, there is just one transformation from shape A to shape B: dilate A by 1/2, followed by a 180 degree rotation.

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Answer:

Step-by-step explanation:

i don't know

do not bother answering with these answers I have already checked none of them have the correct answer

bye children

The distance between two points in a two-dimensional coordinate system represents the length of the shortest path between those two points. This length is also called the Euclidean distance, it is a measure of the straight-line distance between two points.

In other words, it is the length of the line segment connecting the two points. It is calculated using the distance formula which is derived from the Pythagorean theorem, it is calculated as the square root of the sum of the squares of the differences of the coordinates of the two points.

The distance between two points is always a positive value and it is a scalar quantity, it does not have any direction associated with it. It is a measure of the separation between two points, regardless of the direction of the line connecting them.

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Answer:The American colonies declared independence from British rule in 1776 because they were seeking to establish themselves as a sovereign nation, separate from British control and governance.

The colonies had grown increasingly discontent with British rule and policies, particularly those related to taxation and trade. The colonists felt that they were not being fairly represented in British government and that the laws and taxes imposed on them by Britain were unjust and burdensome.

In 1765, the British Parliament passed the Stamp Act, which placed a tax on printed materials such as newspapers, legal documents, and books. The colonists saw this as a violation of their rights as British citizens, as they had no representation in Parliament and felt that they were being taxed without their consent. This led to widespread protests and resistance to the tax, known as the Stamp Act riots.

In 1773, the British government passed the Tea Act, which granted a monopoly on the sale of tea to the British East India Company and imposed taxes on tea imported to the colonies. This led to the famous Boston Tea Party, in which colonists dumped 342 chests of tea into the Boston Harbor as a protest against the tax.

These and other events, such as the Quartering Acts and the Intolerable Acts, which were designed to punish the colonies for their resistance, further fueled the colonists' anger and resentment towards British rule.

In 1774, the First Continental Congress was held, in which representatives from the colonies met to discuss a unified response to British policies. The Congress adopted a Declaration of Rights and Grievances, in which they demanded that their rights as British citizens be respected and that they be given fair representation in Parliament.

In 1775, the American Revolutionary War broke out between the colonies and Great Britain. On July 4, 1776, the Second Continental Congress adopted the Declaration of Independence, which stated that the colonies were no longer subject to British rule

Step-by-step explanation:

Answer: The colonists joined together to fight Britain and gain independence.

Step-by-step explanation: Many colonists were angry because no one represented their needs in the British government. Colonists believed they did not have self-government. The British forced colonists to allow British soldiers to sleep and eat in their homes.

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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Answer:

(1, -9)

Step-by-step explanation:

The slope-intercept formula of a line is: y = mx + b

m = slope

b = y-intercept

We know one point already.

3 = 3(5) + b

3 = 15 + b

3 - 15 = 15 - 15 + b

-12 = b

So now we know the formula: y = 3x - 12

We can plug in 1 as x to find another point

y = 3(1) - 12

y = 3 - 12

y = -9