Find the Equation Using Point-Slope Formula (7,-1) , (-8,-9)

$(7, - 1)$ , $(- 8, - 9)$

Step 1

Find the slope of the line between $(7, - 1)$ and $(- 8, - 9)$ 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.

$m = \frac{- 9 - (- 1)}{- 8 - (7)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{- 9 + 1}{- 8 - (7)}$

Add $- 9$ and $1$ .

$m = \frac{- 8}{- 8 - (7)}$

Simplify the denominator.

Multiply $- 1$ by $7$ .

$m = \frac{- 8}{- 8 - 7}$

Subtract $7$ from $- 8$ .

$m = \frac{- 8}{- 15}$

Dividing two negative values results in a positive value.

$m = \frac{8}{15}$

Step 2

Use the slope $\frac{8}{15}$ and a given point $(7, - 1)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 1) = \frac{8}{15} \cdot (x - (7))$

Step 3

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

$y + 1 = \frac{8}{15} \cdot (x - 7)$

Step 4

Solve for $y$ .

Simplify $\frac{8}{15} \cdot (x - 7)$ .

Rewrite.

$y + 1 = 0 + 0 + \frac{8}{15} \cdot (x - 7)$

Simplify by adding zeros.

$y + 1 = \frac{8}{15} \cdot (x - 7)$

Apply the distributive property.

$y + 1 = \frac{8}{15} x + \frac{8}{15} \cdot - 7$

Combine $\frac{8}{15}$ and $x$ .

$y + 1 = \frac{8 x}{15} + \frac{8}{15} \cdot - 7$

Multiply $\frac{8}{15} \cdot - 7$ .

Combine $\frac{8}{15}$ and $- 7$ .

$y + 1 = \frac{8 x}{15} + \frac{8 \cdot - 7}{15}$

Multiply $8$ by $- 7$ .

$y + 1 = \frac{8 x}{15} + \frac{- 56}{15}$

Move the negative in front of the fraction.

$y + 1 = \frac{8 x}{15} - \frac{56}{15}$

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

Subtract $1$ from both sides of the equation.

$y = \frac{8 x}{15} - \frac{56}{15} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$y = \frac{8 x}{15} - \frac{56}{15} - 1 \cdot \frac{15}{15}$

Combine $- 1$ and $\frac{15}{15}$ .

$y = \frac{8 x}{15} - \frac{56}{15} + \frac{- 1 \cdot 15}{15}$

Combine the numerators over the common denominator.

$y = \frac{8 x}{15} + \frac{- 56 - 1 \cdot 15}{15}$

Simplify the numerator.

Multiply $- 1$ by $15$ .

$y = \frac{8 x}{15} + \frac{- 56 - 15}{15}$

Subtract $15$ from $- 56$ .

$y = \frac{8 x}{15} + \frac{- 71}{15}$

Move the negative in front of the fraction.

$y = \frac{8 x}{15} - \frac{71}{15}$

Step 5

Reorder terms.

$y = \frac{8}{15} x - \frac{71}{15}$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{8}{15} x - \frac{71}{15}$

Point-slope form:

$y + 1 = \frac{8}{15} \cdot (x - 7)$

Step 7

Find the Equation Using Point-Slope Formula (7,-1) , (-8,-9)

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