Find the Slope and y-intercept (-3,2) , (1,-10)

$(- 3, 2)$ , $(1, - 10)$

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.

$m = \frac{- 10 - (2)}{1 - (- 3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $2$ .

$m = \frac{- 10 - 2}{1 - (- 3)}$

Subtract $2$ from $- 10$ .

$m = \frac{- 12}{1 - (- 3)}$

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

$m = \frac{- 12}{1 + 3}$

Add $1$ and $3$ .

$m = \frac{- 12}{4}$

Divide $- 12$ by $4$ .

$m = - 3$

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, $y = m x + b$ .

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

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

$2 = (- 3) \cdot (- 3) + b$

Rewrite the equation as $(- 3) \cdot (- 3) + b = 2$ .

$(- 3) \cdot (- 3) + b = 2$

Multiply $- 3$ by $- 3$ .

$9 + b = 2$

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

Subtract $9$ from both sides of the equation.

$b = 2 - 9$

Subtract $9$ from $2$ .

$b = - 7$

List the slope and y-intercept.

Slope: $- 3$

y-intercept: $(0, - 7)$

Find the Slope and y-intercept (-3,2) , (1,-10)

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