Find the Equation Using Point-Slope Formula (8,-8) and (9,8)

$(8, - 8)$ and $(9, 8)$

Find the slope of the line between $(8, - 8)$ and $(9, 8)$ 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.

$m = \frac{8 - (- 8)}{9 - (8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 8$ .

$m = \frac{8 + 8}{9 - (8)}$

Add $8$ and $8$ .

$m = \frac{16}{9 - (8)}$

Simplify the denominator.

Multiply $- 1$ by $8$ .

$m = \frac{16}{9 - 8}$

Subtract $8$ from $9$ .

$m = \frac{16}{1}$

Divide $16$ by $1$ .

$m = 16$

Use the slope $16$ and a given point $(8, - 8)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 8) = 16 \cdot (x - (8))$

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

$y + 8 = 16 \cdot (x - 8)$

Solve for $y$ .

Simplify $16 \cdot (x - 8)$ .

Rewrite.

$y + 8 = 0 + 0 + 16 \cdot (x - 8)$

Simplify by adding zeros.

$y + 8 = 16 \cdot (x - 8)$

Apply the distributive property.

$y + 8 = 16 x + 16 \cdot - 8$

Multiply $16$ by $- 8$ .

$y + 8 = 16 x - 128$

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

Subtract $8$ from both sides of the equation.

$y = 16 x - 128 - 8$

Subtract $8$ from $- 128$ .

$y = 16 x - 136$

List the equation in different forms.

Slope-intercept form:

$y = 16 x - 136$

Point-slope form:

$y + 8 = 16 \cdot (x - 8)$

Find the Equation Using Point-Slope Formula (8,-8) and (9,8)

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