Find the Equation Using Point-Slope Formula (-8,-10) , (0,-5)

$(- 8, - 10)$ , $(0, - 5)$

Step 1

Find the slope of the line between $(- 8, - 10)$ and $(0, - 5)$ 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.

$m = \frac{- 5 - (- 10)}{0 - (- 8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 10$ .

$m = \frac{- 5 + 10}{0 - (- 8)}$

Add $- 5$ and $10$ .

$m = \frac{5}{0 - (- 8)}$

Simplify the denominator.

Multiply $- 1$ by $- 8$ .

$m = \frac{5}{0 + 8}$

Add $0$ and $8$ .

$m = \frac{5}{8}$

Step 2

Use the slope $\frac{5}{8}$ and a given point $(- 8, - 10)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 10) = \frac{5}{8} \cdot (x - (- 8))$

Step 3

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

$y + 10 = \frac{5}{8} \cdot (x + 8)$

Step 4

Solve for $y$ .

Simplify $\frac{5}{8} \cdot (x + 8)$ .

Rewrite.

$y + 10 = 0 + 0 + \frac{5}{8} \cdot (x + 8)$

Simplify by adding zeros.

$y + 10 = \frac{5}{8} \cdot (x + 8)$

Apply the distributive property.

$y + 10 = \frac{5}{8} x + \frac{5}{8} \cdot 8$

Combine $\frac{5}{8}$ and $x$ .

$y + 10 = \frac{5 x}{8} + \frac{5}{8} \cdot 8$

Cancel the common factor of $8$ .

Cancel the common factor.

$y + 10 = \frac{5 x}{8} + \frac{5}{8} \cdot 8$

Rewrite the expression.

$y + 10 = \frac{5 x}{8} + 5$

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

Subtract $10$ from both sides of the equation.

$y = \frac{5 x}{8} + 5 - 10$

Subtract $10$ from $5$ .

$y = \frac{5 x}{8} - 5$

Step 5

Reorder terms.

$y = \frac{5}{8} x - 5$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{5}{8} x - 5$

Point-slope form:

$y + 10 = \frac{5}{8} \cdot (x + 8)$

Step 7

Find the Equation Using Point-Slope Formula (-8,-10) , (0,-5)

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