Find the Equation Using Point-Slope Formula (9,-9) , (10,-5)

$(9, - 9)$ , $(10, - 5)$

Step 1

Find the slope of the line between $(9, - 9)$ and $(10, - 5)$ 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.

$m = \frac{- 5 - (- 9)}{10 - (9)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 9$ .

$m = \frac{- 5 + 9}{10 - (9)}$

Add $- 5$ and $9$ .

$m = \frac{4}{10 - (9)}$

Simplify the denominator.

Multiply $- 1$ by $9$ .

$m = \frac{4}{10 - 9}$

Subtract $9$ from $10$ .

$m = \frac{4}{1}$

Divide $4$ by $1$ .

$m = 4$

Step 2

Use the slope $4$ and a given point $(9, - 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 9) = 4 \cdot (x - (9))$

Step 3

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

$y + 9 = 4 \cdot (x - 9)$

Step 4

Solve for $y$ .

Simplify $4 \cdot (x - 9)$ .

Rewrite.

$y + 9 = 0 + 0 + 4 \cdot (x - 9)$

Simplify by adding zeros.

$y + 9 = 4 \cdot (x - 9)$

Apply the distributive property.

$y + 9 = 4 x + 4 \cdot - 9$

Multiply $4$ by $- 9$ .

$y + 9 = 4 x - 36$

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

Subtract $9$ from both sides of the equation.

$y = 4 x - 36 - 9$

Subtract $9$ from $- 36$ .

$y = 4 x - 45$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 4 x - 45$

Point-slope form:

$y + 9 = 4 \cdot (x - 9)$

Step 6

Find the Equation Using Point-Slope Formula (9,-9) , (10,-5)

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