Find the Slope and y-intercept (-1.5,-12.5) , (0,-8)

$(- 1.5, - 12.5)$ , $(0, - 8)$

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.

$m = \frac{- 8 - (- 12.5)}{0 - (- 1.5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 12.5$ .

$m = \frac{- 8 + 12.5}{0 - (- 1.5)}$

Add $- 8$ and $12.5$ .

$m = \frac{4.5}{0 - (- 1.5)}$

Simplify the denominator.

Multiply $- 1$ by $- 1.5$ .

$m = \frac{4.5}{0 + 1.5}$

Add $0$ and $1.5$ .

$m = \frac{4.5}{1.5}$

Divide $4.5$ by $1.5$ .

$m = 3$

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, $y = m x + b$ .

$y = (3) \cdot (- 1.5) + b$

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

$- 12.5 = (3) \cdot (- 1.5) + b$

Rewrite the equation as $(3) \cdot (- 1.5) + b = - 12.5$ .

$(3) \cdot (- 1.5) + b = - 12.5$

Multiply $3$ by $- 1.5$ .

$- 4.5 + b = - 12.5$

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

Add $4.5$ to both sides of the equation.

$b = - 12.5 + 4.5$

Add $- 12.5$ and $4.5$ .

$b = - 8$

Step 3

List the slope and y-intercept.

Slope: $3$

y-intercept: $(0, - 8)$

Step 4

Find the Slope and y-intercept (-1.5,-12.5) , (0,-8)

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