Write in Slope-Intercept Form (-3,-28) , (0,-4) , (4,168) , (-5,-174)

$(- 3, - 28)$ , $(0, - 4)$ , $(4, 168)$ , $(- 5, - 174)$

Step 1

Find the slope of the line between $(- 3, - 28)$ and $(0, - 4)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 4 - (- 28)}{0 - (- 3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 28$ .

$m = \frac{- 4 + 28}{0 - (- 3)}$

Add $- 4$ and $28$ .

$m = \frac{24}{0 - (- 3)}$

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

$m = \frac{24}{0 + 3}$

Add $0$ and $3$ .

$m = \frac{24}{3}$

Divide $24$ by $3$ .

$m = 8$

Step 2

Use the slope $8$ and a given point $(- 3, - 28)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 28) = 8 \cdot (x - (- 3))$

Step 3

Simplify the equation and keep it in point-slope form.

$y + 28 = 8 \cdot (x + 3)$

Step 4

Solve for $y$ .

Simplify $8 \cdot (x + 3)$ .

Rewrite.

$y + 28 = 0 + 0 + 8 \cdot (x + 3)$

Simplify by adding zeros.

$y + 28 = 8 \cdot (x + 3)$

Apply the distributive property.

$y + 28 = 8 x + 8 \cdot 3$

Multiply $8$ by $3$ .

$y + 28 = 8 x + 24$

Move all terms not containing $y$ to the right side of the equation.

Subtract $28$ from both sides of the equation.

$y = 8 x + 24 - 28$

Subtract $28$ from $24$ .

$y = 8 x - 4$

Step 5

Write in Slope-Intercept Form (-3,-28) , (0,-4) , (4,168) , (-5,-174)

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