Find the Slope and y-intercept (-8,-1) , (-6,5)

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

Step 1

Find the value of the slope.

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

Find the value of the y-intercept.

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (3) \cdot x + b$

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (3) \cdot (- 8) + b$

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$- 1 = (3) \cdot (- 8) + b$

Rewrite the equation as $(3) \cdot (- 8) + b = - 1$ .

$(3) \cdot (- 8) + b = - 1$

Multiply $3$ by $- 8$ .

$- 24 + b = - 1$

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

Add $24$ to both sides of the equation.

$b = - 1 + 24$

Add $- 1$ and $24$ .

$b = 23$

Step 3

List the slope and y-intercept.

Slope: $3$

y-intercept: $(0, 23)$

Step 4

Find the Slope and y-intercept (-8,-1) , (-6,5)

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