Find the Equation Using Point-Slope Formula (-2,-20) , (9,79)

$(- 2, - 20)$ , $(9, 79)$

Step 1

Find the slope of the line between $(- 2, - 20)$ and $(9, 79)$ 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.

$m = \frac{79 - (- 20)}{9 - (- 2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 20$ .

$m = \frac{79 + 20}{9 - (- 2)}$

Add $79$ and $20$ .

$m = \frac{99}{9 - (- 2)}$

Simplify the denominator.

Multiply $- 1$ by $- 2$ .

$m = \frac{99}{9 + 2}$

Add $9$ and $2$ .

$m = \frac{99}{11}$

Divide $99$ by $11$ .

$m = 9$

Step 2

Use the slope $9$ and a given point $(- 2, - 20)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 20) = 9 \cdot (x - (- 2))$

Step 3

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

$y + 20 = 9 \cdot (x + 2)$

Step 4

Solve for $y$ .

Simplify $9 \cdot (x + 2)$ .

Rewrite.

$y + 20 = 0 + 0 + 9 \cdot (x + 2)$

Simplify by adding zeros.

$y + 20 = 9 \cdot (x + 2)$

Apply the distributive property.

$y + 20 = 9 x + 9 \cdot 2$

Multiply $9$ by $2$ .

$y + 20 = 9 x + 18$

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

Subtract $20$ from both sides of the equation.

$y = 9 x + 18 - 20$

Subtract $20$ from $18$ .

$y = 9 x - 2$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 9 x - 2$

Point-slope form:

$y + 20 = 9 \cdot (x + 2)$

Step 6

Find the Equation Using Point-Slope Formula (-2,-20) , (9,79)

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