Find the Slope and y-intercept (3,-9) , (-1,3)

$(3, - 9)$ , $(- 1, 3)$

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.

$m = \frac{3 - (- 9)}{- 1 - (3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 9$ .

$m = \frac{3 + 9}{- 1 - (3)}$

Add $3$ and $9$ .

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

Simplify the denominator.

Multiply $- 1$ by $3$ .

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

Subtract $3$ from $- 1$ .

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

Divide $12$ by $- 4$ .

$m = - 3$

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, $y = m x + b$ .

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

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

$- 9 = (- 3) \cdot (3) + b$

Rewrite the equation as $(- 3) \cdot (3) + b = - 9$ .

$(- 3) \cdot (3) + b = - 9$

Multiply $- 3$ by $3$ .

$- 9 + b = - 9$

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

Add $9$ to both sides of the equation.

$b = - 9 + 9$

Add $- 9$ and $9$ .

$b = 0$

Step 3

List the slope and y-intercept.

Slope: $- 3$

y-intercept: $(0, 0)$

Step 4

Find the Slope and y-intercept (3,-9) , (-1,3)

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