Find the Slope and y-intercept (6,0) , (3,8)

$(6, 0)$ , $(3, 8)$

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.

$m = \frac{8 - (0)}{3 - (6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{8 + 0}{3 - (6)}$

Add $8$ and $0$ .

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

Simplify the denominator.

Multiply $- 1$ by $6$ .

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

Subtract $6$ from $3$ .

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

Move the negative in front of the fraction.

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

Find the value of the y-intercept.

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

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

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, $y = m x + b$ .

$0 = (- \frac{8}{3}) \cdot (6) + b$

Rewrite the equation as $(- \frac{8}{3}) \cdot (6) + b = 0$ .

$(- \frac{8}{3}) \cdot (6) + b = 0$

Simplify each term.

Cancel the common factor of $3$ .

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

$\frac{- 8}{3} \cdot 6 + b = 0$

Factor $3$ out of $6$ .

$\frac{- 8}{3} \cdot (3 (2)) + b = 0$

Cancel the common factor.

$\frac{- 8}{3} \cdot (3 \cdot 2) + b = 0$

Rewrite the expression.

$- 8 \cdot 2 + b = 0$

Multiply $- 8$ by $2$ .

$- 16 + b = 0$

Add $16$ to both sides of the equation.

$b = 16$

List the slope and y-intercept.

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

y-intercept: $(0, 16)$

Find the Slope and y-intercept (6,0) , (3,8)

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