Find the Slope and y-intercept (4,-8) , (8,5)

$(4, - 8)$ , $(8, 5)$

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.

$m = \frac{5 - (- 8)}{8 - (4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 8$ .

$m = \frac{5 + 8}{8 - (4)}$

Add $5$ and $8$ .

$m = \frac{13}{8 - (4)}$

Simplify the denominator.

Multiply $- 1$ by $4$ .

$m = \frac{13}{8 - 4}$

Subtract $4$ from $8$ .

$m = \frac{13}{4}$

Step 2

Find the value of the y-intercept.

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

$y = (\frac{13}{4}) x + b$

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

$y = (\frac{13}{4}) \cdot (4) + b$

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

$- 8 = (\frac{13}{4}) \cdot (4) + b$

Rewrite the equation as $(\frac{13}{4}) \cdot (4) + b = - 8$ .

$(\frac{13}{4}) \cdot (4) + b = - 8$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{13}{4} \cdot 4 + b = - 8$

Rewrite the expression.

$13 + b = - 8$

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

Subtract $13$ from both sides of the equation.

$b = - 8 - 13$

Subtract $13$ from $- 8$ .

$b = - 21$

Step 3

List the slope and y-intercept.

Slope: $\frac{13}{4}$

y-intercept: $(0, - 21)$

Step 4

Find the Slope and y-intercept (4,-8) , (8,5)

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