Answer:
Given, x²+y²+4X −2y= −1
⇒x²+4x+y²=−1
⇒(x²+4x+4)+(y² −2y+1) =−1+4+1
⇒(x+2)²+(y−1) = 2²
Clearly, = (−2,1)
Radius = 2
The radius of the circle is 2. Therefore, A) is the answer
How to find the radius of the circle using the equation?
The standard form of the equation of a circle is
(x-a)² + (y-b)² = r²
where (a, b) is the center and r is the radius
Given the equation of the circle as x² + y² + 4x - 2y = -1
Factorize the equation using the completing square:
x² + y² + 4x - 2y = -1
x² + 4x + (2)² + y² - 2y + (-1)² = -1 + (2)² + (-1)²
(x+2)² + (y-1)² = -1 + 4 + 1
(x+2)² + (y-1)² = 4
(x+2)² + (y-1)² = 2²
Comparing this equation with (x-a)² + (y-b)² = r²:
r = 2
Thus, the radius of the circle is 2
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Lanren ran 2.76. Miles in a track event. Then she ran 0.4 Mile home after the event. Which model represents the sum of the number of miles lauren ran?
Addition is used to find the sum of the number of miles lauren ran
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Lanren ran 2.76. Miles in a track event.
Then she ran 0.4 Mile home after the event
We need to find the sum of the number of miles lauren ran.
By addition we find the sum of the number of miles lauren ran.
Two point seven six plus zero point four
2.76+0.4
Three point one six
3.16
Hence, addition is used to find the sum of the number of miles lauren ran
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Which models represent 56 as a sum of fractions with a common denominator of 6?
Answer:
Use a model to find the sum of two fractions with the same denominator
Add fractions with a common denominator without a model
Add fractions with a common denominator that contain a variable
Step-by-step explanation:
j
how do you find the range of a graph
Answer:
look at the y axis. :)
Mrs. Wu's car is completely out of gas. Gas costs $3.56 per gallon, and the car's gas tank can hold 12.5 gallons. How much money will Mrs. Wu spend to fill the gas tank?
Answer:It will cost Mrs. Wu $44.5 to fill the gas tank.
Step-by-step explanation: 3.56x12.5= 44.5
graph the line that passes through the points (0,-8) and (5,-5) and determine the equation of the line
*I can graph it, I just need the equation*
The linear equation that passes through the points (0,-8) and (5,-5) is:
y = (3/5)*x - 8
How to find the equation of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
Here we have the two points: (0,-8) and (5,-5)
Then the slope is:
a = (-5 + 8)/(5 - 0) = 3/5
And because of the point (0, -8) we know that the y-intercept is -8, then the linear equation is:
y = (3/5)*x - 8
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EACH OF THE GREEN EQUATIONS HAS A
SOLUTION THAT MATCHES THE
SOLUTION OF A BLUE EQUATION.
RECORD THE MATCHING PAIRS OF
EQUATIONS AND THEIR SOLUTIONS IN
THE PURPLE BOX AT THE RIGHT.
A
5(3x-2) = 4(2x + 1)
D
-x + 3 = 2(x + 15)
B
Cards A and
Cards B and
Cards C and
-4x=-(10x+18)
E
-3(x + 4) = 6(-x - 1)
C
f
are true when x =
are true when x=
are true when x =
2.5x = 5(4x+12)
4x-20= -2(-3x+22)
Answer:
The answer should be A.
Step-by-step explanation:
Answer:
Step-by-step explanation:
what is the minimum sample size required to estimate a population mean with a confidence of 95%, if the margin of error is 2 units and a standard deviation of 10 units? show formula and your calculations. round to the next whole number.
The minimum sample size required to estimate a population mean with a confidence of 95%, a margin error of 2 units and a standard deviation of 10 units is 96.
A minimum sample size is the number of participants one needs to maintain their target confidence interval (margin of error) and confidence level while obtaining results that accurately represent the population they are studying.
The formula to calculate the minimum sample size for the population mean is [tex]\bold{n=\left(\frac{z\times \sigma}{E}\right)^2}[/tex]. Here, n is the sample size, z is the confidence level, σ is the standard deviation, and E is the margin error.
Given, the z-value for 95% confidence is 1.96, E is 2 and σ is 10.
Then, the minimum sample size is,
[tex]\begin{aligned}n&=\left(\frac{1.96\times10}{2}\right)^2\\&=(9.8)^2\\&=96.04\\&\approx96\end{aligned}[/tex]
The answer is 96.
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In the diagram below, \overline{EF}
EF
is parallel to \overline{BC}
BC
. If DC=27DC=27, EF=27.5EF=27.5, and BC=49.5BC=49.5, find the length of \overline{DF}
DF
. Figures are not necessarily drawn to scale.
)
Applying the AA similarity theorem, the length of DF is: 15 units.
What is the AA Similarity Theorem?When two angles in one triangle are congruent to the corresponding two angles in another triangle, both are said to be similar to one another. This means that, the corresponding sides of these two triangles would be proportional or have the same ratio.
In the image attached bellow, triangle DEF and triangle DBC are similar to each other because they have two pairs of corresponding angles that are congruent which are:
<DFE ≅ <DCB [right angles are equal]
<EDF ≅ <BDC [reflexive property of congruence]
Therefore, their corresponding sides will have equal ratios such as:
DC/DF = BC/EF
Substitute:
27/DF = 49.5/27.5
Cross multiply:
DF = (27.5 * 27) / 49.5
DF = 15
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skye is laying a brick barrier around a circular flower bed with a radius of 4 yards. Which of the following expression can be used to find the circumference around the flower bed in yards? Circle ALL that apply.
A 2xn B 4xn C 2x4xn D 8xn
The circumference around the flower bed in yards is D) 8×π.
What is the circumference of the circle?
The circumference of a circle is defined as the linear distance around it.
The formula for the circumference of a circle is [tex]2\pi r[/tex]. Where r is the radius of the circle.
It is given that the radius of the flower bed is 4 yards.
The flower bed is in the shape of a circle.
The circumference of the flower bed is 2×π×r.
Substitute the value of r in the equation.
Therefore the circumference around the flower bed is 8×π.
The correct option is D) 8×π.
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franz and his friends are using the spinners below to play a game. if one turn consists of spinning each spinner once, which table shows all the possible outcomes for one turn?
The possible outcomes for one turn is a table with 4 columns and 3 rows. First Spinner is the label for the columns, and Second Spinner is the label for the rows. Entries 2 A, 2 B, and 2 C are in Column 1. 4A, 4B, and 4C are the entries in Column 2. 6A, 6B, and 6C are entries in column 3. 8A, 8B, and 8C are the entries in column 4. a 2-row, 4-column table.
How many possible outcomes are there in the spinner?The spinner is divided into a total of 8 pieces. Consequently, there are 8 total outcomes. We express our likelihood as a fraction out of 8No. There are seven components overall and one white piece. There are eight possibilities each time you spin the spinner (1-8). One of these eight options is for you to land on the number 8. So, it has an 18 percent chance of happening. Every rotation is distinct. The sum of the results from each event will give you the total number of outcomes for two or more events. The reason why this entails multiplication to find a product is why it is known as the "product rule for counting." Every time, one fourth of the time, the spinner will land on a different color.To the complete question is
franz and his friends are using the spinners below to play a game. if one turn consists of spinning each spinner once, which table shows all the possible outcomes for one turn?
1. A 4-column table with 2 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B. Column 2 has entries 4 A, 4 B. Column 3 has entries 6 A, 6 B. Column 4 has entries 8 A, 8 B.
2. A 4-column table with 3 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B, 2 C. Column 2 has entries 4 A, 4 B, 4 C. Column 3 has entries 6 A, 6 B, 6 C. Column 4 has entries 8 A, 8 B, 8 C. A 4-column table with 2 rows.
3.The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2, A. Column 2 has entries 4, B. Column 3 has entries 6, C. Column 4 has entries 8, D. A 4-column table with 3 rows.
4.The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 A, 2 A. Column 2 has entries 4 B, 4 B, 4 B. Column 3 has entries 6 C, 6 C, 6 C. Column 4 has entries 8 A, 8 B, 8 C.
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Which pair of triangles is congruent by AAS? ∆PQT and ∆RQT
∆TPR and ∆SPR
∆PQU and ∆TSU
∆PRT and ∆PQT
What is the solution to 1/2 |x| = -3?
Answer: 1/2 |x| = -3?
Step-by-step explanation:
about 10% of the population has a particular genetic mutation. 800 people are randomly selected. find the mean for the number of people with the genetic mutation in such groups of 800.
The mean number of people with the genetic mutation in these groups is 80 as this follows a Binomial Distribution.
It is given that 10% of the population has a genetic mutation. We have a sample of 800 here.
Let X be the random variable that defines the number of people with the mutation in the sample.
Since every person can or can't have the mutation, this is a Binomial distribution.
Here,
n = 800
p = 0.1
According to the formula for a Binomial Distribution,
the mean = np
Therefore, the mean for the above distribution will be
800 X 0.1
= 80.
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a 97% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. a preliminary sample standard deviation is 2.1. the smallest sample size n that provides the desired accuracy is
There will be "sample size."=102 Below is an additional explanation.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
hence, There will be "sample size."=102 Below is an additional explanation.
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A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
The final temperature is calculated to be 41.8 degrees Celcius if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa
The final temperature can be calculated by using the combined gas law as follows;
[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]
Here [tex]P_{1}[/tex] and [tex]P_{2}[/tex] represent the initial and final pressure respectively,
[tex]V_{1}[/tex] and [tex]V_{2}[/tex] represent the initial and final volume respectively
[tex]T_{1}[/tex] and [tex]T_{2}[/tex] represent the initial and final temperature respectively
Converting [tex]T_{1}[/tex] to kelvin as follows;
[tex]T_{1}[/tex] = 27 degrees Celcius = 27 + 273 = 300 K
Now the final temperature can be determined by substituting the values in this equation of the combined gas law as follows;
(0.50×10^5)(1.25) / 300 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 ([tex]T_{2}[/tex]) = (0.82×10^5)(0.80)
[tex]T_{2}[/tex] = (0.82×10^5)(0.80) ÷ 208.333333333
[tex]T_{2}[/tex] = 314.8 K
Converting K to degree Celcius as follows;
[tex]T_{2}[/tex] = 314.8 - 273 = 41.8 degree Celcius
Hence 41.8 degrees Celcius is calculated to be the final temperature.
Although a part of your question is incorrect, you might be referring to this question:
A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
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Sarah is trying to find the best deal for her phone service. She narrowed down the choices to the two companies in the table. Both companies charge per-minute rates, and there are no additional costs.
A 2-column table with 2 rows. Column 1 is labeled Company A with entries 18 dollars, 120 minutes. Column 2 is labeled Company B with entries 21 dollars, 150 minutes.
Sarah wants to know which company costs the least amount per minute.
Which quotients should Sarah find? Check all that apply.
StartFraction 120 Over 8 EndFraction
StartFraction 18 Over 120 EndFraction
StartFraction 150 Over 21 EndFraction
StartFraction 21 Over 150 EndFraction
For Sarah to know the company that costs the least amount per minute, the quotients she should find are:
B. 18/120D. 21/150.What is the quotient?The quotient is the result of a division operation.
A division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
A division operation has four parts:
The dividend (the number or value being divided or numerator).The divisor (the number or value dividing or denominator).The equal symbol (showing that the solution is equal to the mathematical expressions).The quotient (the result of the division operation).Company A Company B
Total charge $18 $21
Total minutes 120 150
Per-minute rate $0.15 ($18/120) $0.14 ($21/150)
Thus, the quotients Sarah should find are Options B and D.
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Anne bought a television for 75% off she spent 24 dollars what was the original price
the original price was "x", which oddly enough is the 100%.
now, we know the TV is 75% off, that means the sale price is 100% - 75% = 25%, and we know that's 24 bucks.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 24& 25 \end{array} \implies \cfrac{x}{24}~~=~~\cfrac{100}{25} \implies \cfrac{ x }{ 24 } ~~=~~ 4\implies x=96[/tex]
How many kilometers are in 40miles
Answer:
Below
Step-by-step explanation:
I do not know which conversion factor you are to use, but here is one:
1 km = .62137 mi
then 40 miles becomes :
40 miles / ( .62137 mi / km) = 64.4 km
In a circle, an angle measuring 8.7 radians intercepts an arc of length 3.9. Find the radius of the circle to the nearest 10th.
Answer:
r = .5 units
Step-by-step explanation:
8.7 R is an improper FRACTION of the 2 pi R of the entire circle ....set up a ratio:
8.7 / (2 pi) = 3.9 / x where x is the entire circumference measurement
x = 3.9 / (8.7 / (2 pi) ) = 2.82 units
To find the radius circumf = 2 pi r
2.82 = 2 pi r shows r = .5 units
In AGHI, GI is extended through point I
to point J, m/IGH = (x+16)°,
m/HIJ = (4x – 12)°, and
m/GHI= (x +10)°. Findm/GHI.
Applying the exterior angles theorem, the measure of angle GHI is: 29°.
What is the Exterior Angle Theorem?The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
In other words, if a triangle, for example triangle GHI, has angles G, H, and I, and angle HIJ is the exterior angle formed by extending side GI through point I to point J, then the measure of angle HIJ is equal to the sum of the measures of angles IGH and GHI.
Given the following:
m<IGH = (x+16)°,
m<HIJ = (4x – 12)°,
m<GHI= (x +10)°
Therefore:
m<HIJ = m<IGH + m<GHI
Substitute:
4x - 12 = x + 16 + x + 10
4x - 12 = 2x + 26
4x - 2x = 12 + 26
2x = 38
2x/2 = 38/2
x = 19
m<GHI= (x +10)° = 19 + 10 = 29°
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15 postcards and 10 envelopes = $1.7 envelope is 0.02 cents more expensive than postcard
Answer:
post cards cost .06 each and envelopes cost .08 each.
Step-by-step explanation:
Let p = the cost of the post cards
Let e = the cost of the envelopes
15p + 10e = 1.70
e = p + .02 Substitute p + .02 for e in the first equation
15p + 10(p + .02) = 1.70 Distribute the 10
15p + 10p + .2 = 1.70 Combine like terms
25p + .2 = 1.70 Subtract .2 from both sides
25p = 1.50 Divide both sides by 25
p = .06
Post cards cost .06 each.
Envelopes cost .08 each
Find the vertex of the following function. Write your answer in the form (x, y).
Use the slash mark (/) as a fraction bar if necessary, but do not enter
decimals.
y = x² - 8x+12
Answer here
SUBMIT
The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).
Define parabola.A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. A plane curve created by a point moving so that its distance from a fixed point equals its distance from a fixed line is known as a parabola. A normal parabola's standard equation is y 2 = 4 an x, where an is the distance from the vertex to the focus.
Given,
Function,
y = x² - 8x + 12
The supplied equation's vertex must be located.
The equation is a parabolic equation when we look at it.
We are aware that a parabolic equation's generic form is
y = x² - 8x + 12
where the parabola's vertex's x and y coordinates are denoted by h and k.
We can determine the following by comparing the aforementioned equation with the parabola's general form:
x = 4, y = 4 and h = -8
The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).
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How do you write 0.09 as a fraction?
Answer:
9/100
Step-by-step explanation:
numerator = whole number
denominator = 100
9/100
There are 17 houses on 1 block. How many houses are on 23 blocks?
By using multiplication, it can be calculated that
There are 391 houses in 23 blocks
What is multiplication?
Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.
This is a word problem on multiplication
Number of houses in one block = 17
Assuming there are equal number of houses in each block,
Number of houses in 23 blocks = 23 [tex]\times[/tex] 17 = 391
There are 391 houses in 23 blocks
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write the expression in exponential from 7×7×7×7×7×7
Answer:
7^6
Step-by-step explanation:
7 to the power of 6
Answer: [tex]7^{6}[/tex]
Step-by-step explanation:
Exponential form denotes how many times a value is multiplied by itself.
This is 7 times itself 6 times, so it is written as 7 with a 6 in the top right corner.
The system of conics has two solutions.
What are the solutions to this system of conics?
The points of intersection of the system formed by the circle (x - 2)² + (y - 3)² = 16 and the ellipse (x - 2)² / 16 + (y - 3)² / 64 = 1 are (x₁, y₁) = (- 2, 3) and (x₂, y₂) = (6, 3).
How to determine the points of intersection between two conics
Herein we get a system formed by two conics, the former represents a circle and the latter represents an ellipse. There are different methods to solve the system, the use of graphing tools offers a quick though reasonable approach to find that. First, write the equations corresponding to the conics:
Circle
(x - 2)² + (y - 3)² = 16
Ellipse
(x - 2)² / 16 + (y - 3)² / 64 = 1
Second, plot the two graphs of the functions. (Please see the image attached below)
Third, write the points of intersection:
(x₁, y₁) = (- 2, 3), (x₂, y₂) = (6, 3)
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What is Graph y=-4
y = mx + b
y = -4
m = 0
b = -4
Since the slope (m) is 0, the line is horizontal. The y-intercept (b) is -4, meaning that the graph is a horizontal line at y = -4.
See the attached file for the graph.
i'll mark brainliest!!!!!!
The solution is Option D.
The equation of line that passes through the point P ( 4 , -3 ) and the point Q ( 0 , -2 ) is y = ( -1/4 )x - 2
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first point be P = P ( 4 , -3 )
Let the second point be Q = Q ( 0 , -2 )
Now , the slope of the line passing through the points is calculated from the formula slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( -2 - ( -3 ) ) / ( 0 - 4 )
Slope m = ( -2 + 3 ) / -4
Slope m = -1/4
Now , the equation of line is given by
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - ( -3 ) = ( -1/4 ) ( x - 4 )
On simplifying the equation , we get
y + 3 = ( -1/4 )x + 1
Subtracting 3 on both sides of the equation , we get
y = ( -1/4 )x - 2
Therefore , the value of A is y = ( -1/4 )x - 2
Hence , the equation of line is y = ( -1/4 )x - 2
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which functions have a zero at x equals 4? check all that apply. and (x )equals negative 2 x squared minus 18 x minus 40 b. c (x )equals 2 x squared minus 11 x plus 12 c. e (x )equals 3 x cubed plus x squared minus 48 x minus 16 d. a (x )equals x squared minus 3 x minus 28 e. b (x )equals x cubed minus 4 x squared minus x plus 4
The function that have a zero at x = 4 are
f(x) = 2x^2 - 11x + 12 f(x) = 3x^3 + x^2 - 48x - 16 f(x) = x^3 - 4x^2 - x + 4The first function is
f(x) = -2x^2 - 18x - 40
Substitute the value of x = 4
f(4) = -2(4)^2 - 18(4) - 40
= -2(16) - 72 - 40
= -32 - 72 - 40
= -144
The result is not zero
The second function is
f(x) = 2x^2 - 11x + 12
f(4) = 2(4)^2 - 11(4) +12
= 32 - 44 + 12
= 0
The result is zero
The third function is
f(x) = 3x^3 + x^2 - 48x - 16
f(4) = 3(4)^3 + 4^2 - 48(4) - 16
= 192 + 16 - 192 - 16
= 0
The result is zero
The fourth function is
f(x) = x^2 - 3x - 28
f(4) = 4^2 - 3(4) - 28
= 16 - 12 - 28
= -24
The fifth function is
f(x) = x^3 - 4x^2 - x + 4
f(4) = 4^3 - 4(4)^2 - 4 + 4
= 64 - 64 - 4 + 4
= 0
Therefore, the function f(x) = 2x^2 - 11x + 12, f(x) = 3x^3 + x^2 - 48x - 16 and f(x) = x^3 - 4x^2 - x + 4 have zero at x equals 4
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give the equation of the line that goes through the point (5, -2) and has a slope of 0.
When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). B stands in for the y value of the y-intercept point in the formula.
How to calculated the slope intercept?Determine the equation of the line with a slope of 2/3 and a y intercept of (0, 4).
Solution
Step 1: Replace the provided in the formula.
Provided that the slope, m, is given as 2/3 and the y intercept, (0, 4), b = 4.
y = mx + b
y = 2 3 x + 4
2 /3 x – y = - 4
(Note: You must multiply this by the LCD of 3 to fix this since the conventional form does not support fractional numbers.)
3( 2 /3x – y) = (- 4) (- 4)
3/2x – 3y = - 12
This is the line's determined equation.
Verify is the second step.
Utilizing the formula, plot two points. In this example, y1 = 2 and Y2 = -6. 2x - 3y = - 12 2x – 3y = - 12
Let y = 2 Let y = - 6
2x – 3(2) = - 12 2x – 3(-6) = - 12
2x – 6 = - 12 2x + 18 = - 12
2x = - 6 2x = - 30 \sx = - 3 x = - 15
P1 therefore equals (-3, 2) and P2 equals (-15, -6).
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