Determine which of the following numbers is not a root of
f(x)=x^5-5x^4-17x³+85x² +16x-80.

Answer choices:
1. 5
2. -4
3. -5
4. 4

The expression (1 - x)(125 + 80y) gives us the final cost for Hector after applying the coupon, taking into account the surfboard rental fee and the fee per hour for the surfing classes with the instructor.

(1 - x): This represents the remaining percentage after applying the coupon. If the coupon offers a discount of x percent, then (1 - x) represents the percentage of the total cost that Hector has to pay.

(125 + 80y): This represents the original cost without any discounts or coupons. The term 125 represents the surfboard rental fee, and 80y represents the fee per hour that Hector works with the instructor (where y is the number of hours).

(1 - x)(125 + 80y): Multiplying the two terms together gives us the cost after applying the coupon. The expression (1 - x)(125 + 80y) represents the product of the remaining percentage after the coupon and the original cost.

Therefore, the expression (1 - x)(125 + 80y) gives us the final cost for Hector after applying the coupon, taking into account the surfboard rental fee and the fee per hour for the surfing classes with the instructor.

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Answer: My guess is 0

Step-by-step explanation:

Checked with my math teacher

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 2500\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=2500\left[ \cfrac{\left( 1+\frac{0.035}{1} \right)^{1 \cdot 10}-1}{\frac{0.035}{1}} \right]\left(1+\frac{0.035}{1}\right)\\\\\\ A=2500\left[ \cfrac{0.4106}{0.035} \right](1.035)\implies A \approx 30354.98[/tex]

The line segment is calcilated by  the formula  represented mathematically as (x1+x2/2, y1+y2/2), The midpoint is (5,5).

The midpoint of a line segment is the point on the line that is halfway between the endpoints of the line.

To find the midpoint of a line segment, you need to average the x-coordinates of the endpoints and the y-coordinates of the endpoints.

In other words, the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.

The midpoint formula can be represented mathematically as (x1+x2/2, y1+y2/2)

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.

Let's illustrate this with an example:

Suppose we have a line segment with endpoints (2,3) and (8,7).

To find the midpoint of the line segment, we use the formula (x1+x2/2, y1+y2/2)(2+8/2, 3+7/2)(10/2, 10/2)

The midpoint is (5,5).

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To solve for x, we need to isolate x on one side of the equation. We can do this by adding 9 to both sides of the equation:

3x - 1 + 9 = 2x - 9 + 9

3x + 8 = 2x

Now we can subtract 2x from both sides of the equation:

3x - 2x + 8 = 2x - 2x

x + 8 = 0

Finally, we can subtract 8 from both sides of the equation:

x + 8 - 8 = 0 - 8

x = -8

Therefore, x equals -8.

The standard form which are equivalent to the specified factored form of the quadratic equations are;

f(x) = (x + 2)·(x - 6) → B. f(x) = x² - 4·x -12

f(x) = (x - 4)·(x + 3) → D. f(x) = x² - x - 12

f(x) = (x - 12)·(x + 1) → A. f(x) = x² - 11·x - 12

f(x) = (x - 3)·(x + 4) → C. f(x) = x² + x - 12

The factored form of a quadratic function is the expression of the function as the product of the linear factors, which is the form; y = (x + p)·(x + q)

The factored form of the quadratic equations can be expanded to find the equivalent standard form as follows;

f(x) = (x + 2) × (x - 6) = x² - 6·x + 2·x - 12 = x² - 4·x - 12

f(x) = (x - 4) × (x + 3) = x² - 4·x +3·x - 12 = x² - x - 12

f(x) = (x - 12) × (x + 1) = x² - 12·x + x - 12 = x² - 11·x - 12

f(x) = (x - 3) × (x + 4) = x² - 3·x + 4·x - 12 = x² + x - 12

Therefore, we get;

A. f(x) = x² - 11·x - 12 ⇒ f(x) = (x - 12) × (x + 1)

B. f(x) = x² - 4·x - 12 ⇒ f(x) = (x + 2) × (x - 6)

C. f(x) =  x² + x - 12 ⇒ f(x) =  (x - 3) × (x + 4)

D. f(x) = x² - x - 12 ⇒ f(x) = (x - 4) × (x + 3)

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The sky appears blue because of Rayleigh scattering while water appears blue due to selective absorption and scattering of light.

The blue color of the sky is a result of Rayleigh scattering which occurs when the Earth's atmosphere scatters shorter wavelengths of light (blue and violet) more efficiently than longer wavelengths (red and orange).

When sunlight enters the atmosphere, the blue light is scattered in all directions by the molecules and tiny particles present in the air creating the blue appearance of the sky.

Similarly, water appear blue due to selective absorption and scattering of light. Water molecules selectively absorb colors from the visible light spectrum and absorb longer wavelengths (such as red) more effectively than shorter wavelengths (such as blue).

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We know that 20 miles is the distance to tbe airport. So, we should start by substituting the x on each expression with 20.

This way we can find the cost of each ride.

Dave

C=1.8x

C=1.8(20)

C=36

Dave's ride would cost 36 pounds .

Pete

C=1.5x+5

C=1.5(20)+5

C= 30+5

C=35

Pete's ride would cost 35 pounds.

Rick

C=1.9x-3.5

C=1.9(20)-3.5

C=38-3.5

C=34.5

Rick's ride would cost 34.5 pounds.

The cheapest ride would be Rick's Rickshaw.

Now, we just figure out the change .

Jenny has 40 pounds

So, subtracting with the cheapest rate of 34.5:

40-34.5=5.5

Answer. Jenny would get 5.5 pounds in change if she took the cheapest ride.

The answer is:

32.4

Work/explanation:

These numbers need to be multiplied.

[tex]\sf{(540)(0.03)(2)}[/tex]

[tex]\sf{16.2\times2}[/tex]

[tex]\sf{32.4}[/tex]

Hence, the product of these numbers is 32.4.

The y-intercept of g(x) is less than the y-intercept of f(x). The y-intercept of g(x) is -1/2, which is greater than the y-intercept of f(x), which is -4. So, the correct answer is A. The y-intercept of g(x) is less than the y-intercept of f(x).

To determine the y-intercept and x-intercept of the function g(x) = 4/(x - 8), we need to find the values of x for which g(x) equals zero and the value of g(x) when x equals zero.

First, let's find the x-intercept of g(x), which is the value of x for which g(x) equals zero. Setting g(x) = 0 and solving for x, we have:

0 = 4/(x - 8)

This equation has no solutions because a fraction can only be zero if its numerator is zero, but in this case, the numerator (4) is always non-zero. Therefore, g(x) does not have an x-intercept.

Next, let's find the y-intercept of g(x), which is the value of g(x) when x equals zero:

g(0) = 4/(0 - 8)

g(0) = 4/(-8)

g(0) = -1/2

Therefore, the y-intercept of g(x) is -1/2.

Now, let's compare the y-intercepts of g(x) and f(x). From the given table, we see that the y-intercept of f(x) is -4.

Since -4 is not equal to -1/2, we can conclude that statement B, "The y-intercept of g(x) is equal to the y-intercept of f(x)," is false.

To summarize, the correct answer is: A. The y-intercept of g(x) is less than the y-intercept of f(x).

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Answer:

18.75%

Step-by-step explanation:

x/100 = 18/96

96x = 100 × 18

x = 18.75

The solutions to the equation that are given can be seen in options A and E

A quadratic equation is a polynomial equation of the second degree, which means it contains at least one term with an exponent of 2. The general form of a quadratic equation is:

ax^2 + bx + c = 0

In this equation, "x" is the variable, and "a," "b," and "c" are coefficients, where "a" cannot be zero. The coefficients "a," "b," and "c" can be any real numbers, including positive, negative, or zero.

x^2 + 10x +25 =8

x^2 + 10x + 25 - 8 = 0

x^2 + 10x + 17 = 0

x = -5 ± 2√2

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The value of x is $6,666.67.Assume that x equals the amount Seema invested at 3% interest. Also, let us designate the interest from Seema's $4,000 investment at 5% by I1 and the interest from Seema's x dollars investment at 3% by I2.

Simple interest is calculated as Simple Interest = (Principal * Rate * Time)/100.

Because we want to compute the return at the end of the year, we know the time for both investments is one year.

We may write two equations using this formula: I₁ = (4000 * 5 * 1) / 100 = 200I₂ = (x * 3 * 1) / 100 = 0.03x

We also know that Seema's return on investment is the same for both investments. As a result, we may write: I1 = I2 200 = 0.03x

We may now solve for x: x = 200/0.03x = 6666.67.

Therefore, the value of x is $6,666.67.

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Answer:

0.07

Step-by-step explanation:

[tex]\displaystyle Z=\frac{X-\mu}{\sigma}=\frac{95.8-89.7}{87.7}\approx0.07[/tex]

The combination that will successfully tile a flat surface is regular pentagons and regular hexagons (option C).

The correct combination that will tile a flat surface is option C: regular pentagons and regular hexagons.

To understand why this combination works, we need to consider the properties of regular polygons and their ability to tile a plane without gaps or overlaps.

Regular polygons are shapes with equal side lengths and equal angles. For a combination of polygons to tile a flat surface, the polygons must fit together in a way that their sides align perfectly without leaving any gaps or overlaps.

Option A, which suggests using regular heptagons (7-sided polygons) and equilateral triangles, will not tile a flat surface. This is because the angles of the heptagons (internal angles of 128.57 degrees) and the angles of the equilateral triangles (internal angles of 60 degrees) do not add up to a full 360 degrees, which is necessary for tiling a plane.

Option B, proposing squares and regular octagons, will not tile a flat surface either. The internal angles of squares are 90 degrees, while the internal angles of regular octagons are 135 degrees. These angles do not match up, preventing a proper tiling.

Option D, combining regular hexagons and squares, does not work either. Although both regular hexagons and squares have internal angles of 120 degrees and 90 degrees, respectively, they cannot fit together without leaving gaps or overlaps. Attempting to tile with just these two shapes will result in a non-periodic pattern.

Option C, however, presents regular pentagons and regular hexagons. Both polygons have internal angles that add up to 360 degrees, allowing them to fit together perfectly. Specifically, a regular hexagon has internal angles of 120 degrees, while a regular pentagon has internal angles of 108 degrees. By alternating these two shapes, they can fit together to tile a flat surface without any gaps or overlaps.

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The x-intercepts and y-intercepts of the graph are x = 5 and y = 2

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

The x-intercepts are when y = 0

In this case, it is

x = 5

The y-intercepts are when x = 0

In this case, it is

y = 2

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The GDP for the first quarter of 2020 is $120 billion.

To calculate the GDP (Gross Domestic Product) for the first quarter of 2020, we need to consider the components of GDP: consumption (C), investment (I), government spending (G), and net exports (NX). The formula for GDP is:

GDP = C + I + G + NX

Given the following statistics for the first quarter of 2020:

Consumers purchased $50 billion of goods and services (C = $50 billion).

Businesses invested $10 billion back into their businesses and held $5 billion of goods produced during the year in their inventories (I = $10 billion).

Federal, state, and local governments spent $70 billion throughout the year (G = $70 billion).

The nation exported $90 billion worth of goods and services while importing $100 billion.

To calculate net exports (NX), we subtract the value of imports from the value of exports:

NX = Exports - Imports

NX = $90 billion - $100 billion

NX = -$10 billion (negative value indicates a trade deficit)

Now, we can substitute the given values into the GDP formula:

GDP = C + I + G + NX

GDP = $50 billion + $10 billion + $70 billion + (-$10 billion)

GDP = $120 billion.

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The answer is option 4.Triangle ABC is dilated by a scale factor of 1/2 about the origin and then reflected over the x-axis. The location of B” after the sequence of transformations is (5,-3).

A scale factor is a measure of how much an object is stretched or shrunk about a fixed point in the plane. We can dilate a triangle by multiplying its coordinates by a scale factor k, where k is a positive real number.A reflection is a transformation that flips a figure over a line of reflection.

The line of reflection is a perpendicular bisector of the segment connecting a point and its image.The order of these transformations makes a difference in the result. When a triangle is dilated first, and then reflected, we can either reflect the original triangle over the x-axis first and then dilate it by a scale factor of 1/2 about the origin or dilate the original triangle first and then reflect it over the x-axis.

When we first reflect the original triangle over the x-axis, we obtain the image of triangle A'B'C', as shown below:AB has an endpoint at (0, 0) and another at (-10, 6), so we reflect over the x-axis as shown above to get A'B', whose endpoints are (0,0) and (10,-6).We then dilate triangle A'B'C' by a scale factor of 1/2 about the origin as shown below:

The image of B after the two transformations is B''.

To find the coordinates of B'', we take the point (5,-3) as the new origin and translate the image points back to their original position by adding 5 to the x-coordinates and subtracting 3 from the y-coordinates.

The image of B after the two transformations is B'' = (5, -3). Thus, the answer is option 4.

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The complete question is:

content loaded

Triangle abc is dilated by a scale factor of 1/2 about the origin and then reflected over the x-axis. What is the location of B” after the sequence of transformations?

1. (-10, 6)

2.(-5,3)

3.(5,3)

4.(5,-3)

The original mass of the red giant was approximately 13.67 solar masses (MSun).

After 0.8 million years (0.8 * 10⁶ years), the red giant's mass is 11 MSun. This means that it has lost a certain amount of mass over this time period.

The mass loss can be calculated by multiplying the mass loss rate by the time period:

Mass loss = Mass loss rate * Time

Mass loss = (1 MSun / 300,000 years) * (0.8 * 10^6 years)

Mass loss = 2.67 MSun

Now, we can find the original mass by subtracting the mass loss from the current mass:

M original = M current + Mass loss

M original = 11 MSun + 2.67 MSun

M original = 13.67 MSun

Therefore, the original mass of the red giant was approximately 13.67 solar masses (MSun).

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A red giant loses a solar mass in 300,000 years via a superwind. After 0.8 million years, it has a mass of 11MSun. What was its original mass?

The union of P and (Q n R), denoted as P u (Q n R), will contain all the elements from both sets without repetition. Thus, the final set is:

P u (Q n R) = {1, 3, 6, 7, 9, 11}

To find the set P u (Q n R), we need to first calculate the intersection of sets Q and R, and then take the union of set P with the resulting intersection.

The intersection of sets Q and R, denoted as Q n R, contains the elements that are common to both Q and R. From the given sets:

Q = {2, 6, 11}

R = {4, 6, 9, 11}

The intersection Q n R is {6, 11}, as these are the elements present in both sets Q and R.

Now, we can take the union of set P with the intersection Q n R:

P = {1, 3, 7, 9}

Q n R = {6, 11}

The union of P and (Q n R), denoted as P u (Q n R), will contain all the elements from both sets without repetition. Thus, the final set is:

P u (Q n R) = {1, 3, 6, 7, 9, 11}

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The graph of the inequality -2y + 3 < 5 is a shaded region below the line y = -1.

1. Start by rewriting the inequality with y on the left side: -2y + 3 < 5.

2. Subtract 3 from both sides of the inequality: -2y < 2.

3. Divide both sides of the inequality by -2. Since we are dividing by a negative number, the inequality sign flips: y > -1.

4. This means that y must be greater than -1 to satisfy the inequality.

5. To graph this inequality, draw a number line and mark -1 with an open circle (since y is not equal to -1).

6. Shade the region to the right of -1, since y must be greater than -1.

7. Since there are no other variables or coefficients in the inequality, the line y = -1 is a horizontal line passing through -1 on the y-axis.

8. Indicate on the graph that the line itself is not part of the solution by making it a dashed line instead of a solid line.

9. Therefore, the graph of the inequality -2y + 3 < 5 is a shaded region below the line y = -1.

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The slope of the line which is 1/7, and the points (-8, -8), (6, v) indicates that value of v is -6

The slope of a line is the ratio of the rise to the run of the line. The slope of a line that passes through the points (x₁, y₁), and (x₂, y₂), can be presented as follows;

Where;

(x₁, y₁), are the x- and y-coordinate of  one of the points on the line

(x₂, y₂) is the x- and y-coordinate of the other point on the line

The points through which the line passes are (-8, -8), (6, v)

The slope of the line is; 1/7

Therefore, we get;

(x₁, y₁) = (-8, -8)

(x₂, y₂) = (6, v)

Slope of the line = (v - (-8))/(6 - (-8)) = 1/7

(v + 8)/14 = 1/7

7 × (v + 8) = 14 × 1 = 14

7·v + 56 = 14

7·v = 14 - 56 = -42

v = -42/7 = -6

v = -6

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Answer:

The first blank is the less than symbol (<)

The second blank is the greater than symbol (>)

Step-by-step explanation:

It looks like you are comparing the left side of the equation to the right side.

If we look at the first unknown, we can multiply out the numbers on the left side to see if it's equal to the right side.

[tex]2^2 * 4^2 = 64[/tex]

while the right side is this:

[tex]8^4 = 4096[/tex]

we can see that one side is clearly bigger than the other side. Thus, we would use the less than symbol in this case as 64 is less than 4096:

[tex]2^2 * 4^2 < 8^4[/tex]

[tex]64 < 4096[/tex]

We can do the same for the second unknown as well:

[tex]2^4 * 4^2 = 256\\8^2 = 64[/tex]

In this case, we can see that the left side is bigger than the right side. Thus, we will use the greater than symbol as 256 is greater than 64:

[tex]2^4*4*2 > 8^2\\256 > 64[/tex]

The equation of the line passing through the point (2, 3) and making an angle of 45 degrees with the line x - 3y = 5 is

y = -3x + 9.

The equation of a line passing through a given point and making an angle of 45 degrees with another line can be found using the concept of slope.

Let's start by finding the slope of the given line, x - 3y = 5. To do this, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope.

Rearranging the equation, we get:

x - 3y = 5
-3y = -x + 5
y = (1/3)x - (5/3)

So, the slope of the given line is 1/3.

Since the line we want to find makes an angle of 45 degrees with the given line, the slope of the line we want to find will be the negative reciprocal of the slope of the given line. The negative reciprocal of 1/3 is -3.

Now, let's use the point-slope form of a linear equation to find the equation of the line passing through the point (2, 3) with a slope of -3. The point-slope form is given by:

y - y1 = m(x - x1)

Substituting the values into the formula, we get:

y - 3 = -3(x - 2)

Expanding the equation:

y - 3 = -3x + 6

Simplifying:

y = -3x + 9

Therefore, the equation of the line passing through the point (2, 3) and making an angle of 45 degrees with the line x - 3y = 5 is y = -3x + 9.

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Answer:

y > 1/3 x - 3

Step-by-step explanation:

First, we need to find the equation of the dashed line.

The y-intercept, b, is -3.

The slope, m = rise/run = 1/3.

The equation of the line is

y = 1/3 x - 3

The line is dashed, not solid, so we will use < or >, but not ≥ or ≤.

The shading is above the line, so we use >.

Answer: y > 1/3 x - 3

Answer:

To determine the scale factor used, we can compare the corresponding side lengths of the two triangles.

In triangle D, the side lengths are 6, 8, and 10.

In triangle D', the corresponding side lengths are 18, 24, and 30.

To find the scale factor, we can divide the corresponding side lengths of triangle D' by the corresponding side lengths of triangle D.

Side length ratio:

18/6 = 3

24/8 = 3

30/10 = 3

The ratio of corresponding side lengths is consistent at 3 for each pair. Therefore, the scale factor used is 3.

So, the correct answer is 3.

Step-by-step explanation:

Step 1: Identify the corresponding side lengths of the two triangles.

In triangle D, the side lengths are given as 6, 8, and 10.

In triangle D', the corresponding side lengths are given as 18, 24, and 30.

Step 2: Calculate the ratio of each corresponding side length of D' to D.

For the first pair of corresponding sides:

18/6 = 3

For the second pair of corresponding sides:

24/8 = 3

For the third pair of corresponding sides:

30/10 = 3

Step 3: Analyze the ratios obtained.

Since all three ratios are equal to 3, it indicates a consistent scale factor between the corresponding side lengths of the two triangles.

Step 4: Determine the scale factor.

The scale factor is the constant ratio by which each corresponding side length is multiplied to obtain the corresponding side length of the larger triangle. In this case, since the ratio is 3 for all pairs, the scale factor used is 3.

So, the step-by-step explanation confirms that the scale factor used is 3.

Answer:

The scale factor is 3

Step-by-step explanation:

For triangle D to be dilated into triagle D', each side of D is multiplied by 3,i.e,

6 * 3 = 18

8 * 3 = 24

10 * 3 = 30

Therefor, the scale factor to turn triangle D to D' is 3

Answer:

To determine the number of ways a committee can be formed with one representative from each team, you can multiply the number of choices for each team.

Number of choices for the football team = 53

Number of choices for the basketball team = 15

Number of choices for the baseball team = 12

To find the total number of ways, you multiply these numbers together:

53 choices * 15 choices * 12 choices = 9,540 ways

Therefore, there are 9,540 ways to form a committee with one representative from each team.

Step-by-step explanation:

Answer:

The total is 9540

Step-by-step explanation:

Do 128 x 22 say for that it is the 53 and 15 players Then do 127 x 21 which it would be 15 x 14 but you are doing the first number honestly  then 127 x 21 and that would be 12 x 11 so therefore you will multiply it by 53 x 15 x 12 = 9,540

Answer: banana- 88

Orange-55

Apple-143

Step-by-step explanation:

220 divided by 5, times 2,

that’s the banana trees

220 divided by 4, that’s the oranges

Add the answers together

Take the answer away from 220 that’s the apples

Answer:

Equation of the line in slope-intercept form:  y = 2x - 3

Step-by-step explanation:

The general equation of the sloe-intercept form of a line is given by:

y = mx + b, where

Step 1:  Find m, the slope:

We can find m, the slope of the line using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where:

Thus, we can plug in (2, 1) for (x1, y1) and (-1, -5) for (x2, y2) to find m, the slope of the line:

m = (-5 - 1) / (-1 - 2)

m = (-6) / (-3)

m = 2

Thus, the slope of the line is 2.

Step 2:  Find b, the y-intercept of the line:

We can find b, the y-intercept of the line by plugging in any of the two points for (x, y) and 2 for m in the slope-intercept form.  Let's use (2, 1) for (x, y):

1 = 2(2) + b

1 = 4 + b

-3 = b

Thus, the y-intercept of the line is -3.

Therefore, the equation of a line in slope-intercept form passing through the points (2, 1) and (-1, -5) is y = 2x - 3