Find the Slope and y-intercept (-6,5) , (-3,-3)

$(- 6, 5)$ , $(- 3, - 3)$

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.

$m = \frac{- 3 - (5)}{- 3 - (- 6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $5$ .

$m = \frac{- 3 - 5}{- 3 - (- 6)}$

Subtract $5$ from $- 3$ .

$m = \frac{- 8}{- 3 - (- 6)}$

Simplify the denominator.

Multiply $- 1$ by $- 6$ .

$m = \frac{- 8}{- 3 + 6}$

Add $- 3$ and $6$ .

$m = \frac{- 8}{3}$

Move the negative in front of the fraction.

$m = - \frac{8}{3}$

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{8}{3}) \cdot x + b$

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

$y = (- \frac{8}{3}) \cdot (- 6) + b$

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

$5 = (- \frac{8}{3}) \cdot (- 6) + b$

Rewrite the equation as $(- \frac{8}{3}) \cdot (- 6) + b = 5$ .

$(- \frac{8}{3}) \cdot (- 6) + b = 5$

Simplify each term.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$\frac{- 8}{3} \cdot - 6 + b = 5$

Factor $3$ out of $- 6$ .

$\frac{- 8}{3} \cdot (3 (- 2)) + b = 5$

Cancel the common factor.

$\frac{- 8}{3} \cdot (3 \cdot - 2) + b = 5$

Rewrite the expression.

$- 8 \cdot - 2 + b = 5$

Multiply $- 8$ by $- 2$ .

$16 + b = 5$

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

Subtract $16$ from both sides of the equation.

$b = 5 - 16$

Subtract $16$ from $5$ .

$b = - 11$

Step 3

List the slope and y-intercept.

Slope: $- \frac{8}{3}$

y-intercept: $(0, - 11)$

Step 4

Find the Slope and y-intercept (-6,5) , (-3,-3)

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