Find the Slope and y-intercept (6,-20) , (9,-12)

$(6, - 20)$ , $(9, - 12)$

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.

$m = \frac{- 12 - (- 20)}{9 - (6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 20$ .

$m = \frac{- 12 + 20}{9 - (6)}$

Add $- 12$ and $20$ .

$m = \frac{8}{9 - (6)}$

Simplify the denominator.

Multiply $- 1$ by $6$ .

$m = \frac{8}{9 - 6}$

Subtract $6$ from $9$ .

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

Find the value of the y-intercept.

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

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

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, $y = m x + b$ .

$- 20 = (\frac{8}{3}) \cdot (6) + b$

Rewrite the equation as $(\frac{8}{3}) \cdot (6) + b = - 20$ .

$(\frac{8}{3}) \cdot (6) + b = - 20$

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{8}{3} \cdot (3 (2)) + b = - 20$

Cancel the common factor.

$\frac{8}{3} \cdot (3 \cdot 2) + b = - 20$

Rewrite the expression.

$8 \cdot 2 + b = - 20$

Multiply $8$ by $2$ .

$16 + b = - 20$

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

Subtract $16$ from both sides of the equation.

$b = - 20 - 16$

Subtract $16$ from $- 20$ .

$b = - 36$

List the slope and y-intercept.

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

y-intercept: $(0, - 36)$

Find the Slope and y-intercept (6,-20) , (9,-12)

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