Find the Equation Using Point-Slope Formula (-8,-1) and (-6,5)

$(- 8, - 1)$ and $(- 6, 5)$

Step 1

Find the slope of the line between $(- 8, - 1)$ and $(- 6, 5)$ 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.

$m = \frac{5 - (- 1)}{- 6 - (- 8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{5 + 1}{- 6 - (- 8)}$

Add $5$ and $1$ .

$m = \frac{6}{- 6 - (- 8)}$

Simplify the denominator.

Multiply $- 1$ by $- 8$ .

$m = \frac{6}{- 6 + 8}$

Add $- 6$ and $8$ .

$m = \frac{6}{2}$

Divide $6$ by $2$ .

$m = 3$

Step 2

Use the slope $3$ and a given point $(- 8, - 1)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 1) = 3 \cdot (x - (- 8))$

Step 3

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

$y + 1 = 3 \cdot (x + 8)$

Step 4

Solve for $y$ .

Simplify $3 \cdot (x + 8)$ .

Rewrite.

$y + 1 = 0 + 0 + 3 \cdot (x + 8)$

Simplify by adding zeros.

$y + 1 = 3 \cdot (x + 8)$

Apply the distributive property.

$y + 1 = 3 x + 3 \cdot 8$

Multiply $3$ by $8$ .

$y + 1 = 3 x + 24$

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

Subtract $1$ from both sides of the equation.

$y = 3 x + 24 - 1$

Subtract $1$ from $24$ .

$y = 3 x + 23$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 3 x + 23$

Point-slope form:

$y + 1 = 3 \cdot (x + 8)$

Step 6

Find the Equation Using Point-Slope Formula (-8,-1) and (-6,5)

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