Find the Slope and y-intercept (-5,8) , (5,2)

$(- 5, 8)$ , $(5, 2)$

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.

$m = \frac{2 - (8)}{5 - (- 5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $8$ .

$m = \frac{2 - 8}{5 - (- 5)}$

Subtract $8$ from $2$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 5$ .

$m = \frac{- 6}{5 + 5}$

Add $5$ and $5$ .

$m = \frac{- 6}{10}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 6$ and $10$ .

Factor $2$ out of $- 6$ .

$m = \frac{2 (- 3)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$m = \frac{2 \cdot - 3}{2 \cdot 5}$

Cancel the common factor.

$m = \frac{2 \cdot - 3}{2 \cdot 5}$

Rewrite the expression.

$m = \frac{- 3}{5}$

Move the negative in front of the fraction.

$m = - \frac{3}{5}$

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{3}{5}) \cdot x + b$

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

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

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

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

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

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

Simplify each term.

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3}{5}$ into the numerator.

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

Factor $5$ out of $- 5$ .

$\frac{- 3}{5} \cdot (5 (- 1)) + b = 8$

Cancel the common factor.

$\frac{- 3}{5} \cdot (5 \cdot - 1) + b = 8$

Rewrite the expression.

$- 3 \cdot - 1 + b = 8$

Multiply $- 3$ by $- 1$ .

$3 + b = 8$

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

Subtract $3$ from both sides of the equation.

$b = 8 - 3$

Subtract $3$ from $8$ .

$b = 5$

Step 3

List the slope and y-intercept.

Slope: $- \frac{3}{5}$

y-intercept: $(0, 5)$

Step 4

Find the Slope and y-intercept (-5,8) , (5,2)

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