Find the Slope and y-intercept (-5,1) , (5,9)

$(- 5, 1)$ , $(5, 9)$

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.

$m = \frac{9 - (1)}{5 - (- 5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $1$ .

$m = \frac{9 - 1}{5 - (- 5)}$

Subtract $1$ from $9$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 5$ .

$m = \frac{8}{5 + 5}$

Add $5$ and $5$ .

$m = \frac{8}{10}$

Cancel the common factor of $8$ and $10$ .

Factor $2$ out of $8$ .

$m = \frac{2 (4)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$m = \frac{2 \cdot 4}{2 \cdot 5}$

Cancel the common factor.

$m = \frac{2 \cdot 4}{2 \cdot 5}$

Rewrite the expression.

$m = \frac{4}{5}$

Step 2

Find the value of the y-intercept.

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

$y = (\frac{4}{5}) x + b$

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

$y = (\frac{4}{5}) \cdot (- 5) + b$

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

$1 = (\frac{4}{5}) \cdot (- 5) + b$

Rewrite the equation as $(\frac{4}{5}) \cdot (- 5) + b = 1$ .

$(\frac{4}{5}) \cdot (- 5) + b = 1$

Simplify each term.

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$\frac{4}{5} \cdot (5 (- 1)) + b = 1$

Cancel the common factor.

$\frac{4}{5} \cdot (5 \cdot - 1) + b = 1$

Rewrite the expression.

$4 \cdot - 1 + b = 1$

Multiply $4$ by $- 1$ .

$- 4 + b = 1$

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

Add $4$ to both sides of the equation.

$b = 1 + 4$

Add $1$ and $4$ .

$b = 5$

Step 3

List the slope and y-intercept.

Slope: $\frac{4}{5}$

y-intercept: $(0, 5)$

Step 4

Find the Slope and y-intercept (-5,1) , (5,9)

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