Find the Slope and y-intercept (8,0) , (0,2)

$(8, 0)$ , $(0, 2)$

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.

$m = \frac{2 - (0)}{0 - (8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{2 + 0}{0 - (8)}$

Add $2$ and $0$ .

$m = \frac{2}{0 - (8)}$

Simplify the denominator.

Multiply $- 1$ by $8$ .

$m = \frac{2}{0 - 8}$

Subtract $8$ from $0$ .

$m = \frac{2}{- 8}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ and $- 8$ .

Factor $2$ out of $2$ .

$m = \frac{2 (1)}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

$m = \frac{2 \cdot 1}{2 \cdot - 4}$

Cancel the common factor.

$m = \frac{2 \cdot 1}{2 \cdot - 4}$

Rewrite the expression.

$m = \frac{1}{- 4}$

Move the negative in front of the fraction.

$m = - \frac{1}{4}$

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{1}{4}) \cdot x + b$

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

$y = (- \frac{1}{4}) \cdot (8) + b$

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

$0 = (- \frac{1}{4}) \cdot (8) + b$

Rewrite the equation as $(- \frac{1}{4}) \cdot (8) + b = 0$ .

$(- \frac{1}{4}) \cdot (8) + b = 0$

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} \cdot 8 + b = 0$

Factor $4$ out of $8$ .

$\frac{- 1}{4} \cdot (4 (2)) + b = 0$

Cancel the common factor.

$\frac{- 1}{4} \cdot (4 \cdot 2) + b = 0$

Rewrite the expression.

$- 1 \cdot 2 + b = 0$

Multiply $- 1$ by $2$ .

$- 2 + b = 0$

Add $2$ to both sides of the equation.

$b = 2$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{4}$

y-intercept: $(0, 2)$

Step 4

Find the Slope and y-intercept (8,0) , (0,2)

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