Find the Slope and y-intercept (-10,-7) , (-5,-9)

$(- 10, - 7)$ , $(- 5, - 9)$

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.

$m = \frac{- 9 - (- 7)}{- 5 - (- 10)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 7$ .

$m = \frac{- 9 + 7}{- 5 - (- 10)}$

Add $- 9$ and $7$ .

$m = \frac{- 2}{- 5 - (- 10)}$

Simplify the denominator.

Multiply $- 1$ by $- 10$ .

$m = \frac{- 2}{- 5 + 10}$

Add $- 5$ and $10$ .

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

Move the negative in front of the fraction.

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

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{2}{5}) \cdot x + b$

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

$y = (- \frac{2}{5}) \cdot (- 10) + b$

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

$- 7 = (- \frac{2}{5}) \cdot (- 10) + b$

Rewrite the equation as $(- \frac{2}{5}) \cdot (- 10) + b = - 7$ .

$(- \frac{2}{5}) \cdot (- 10) + b = - 7$

Simplify each term.

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{- 2}{5} \cdot - 10 + b = - 7$

Factor $5$ out of $- 10$ .

$\frac{- 2}{5} \cdot (5 (- 2)) + b = - 7$

Cancel the common factor.

$\frac{- 2}{5} \cdot (5 \cdot - 2) + b = - 7$

Rewrite the expression.

$- 2 \cdot - 2 + b = - 7$

Multiply $- 2$ by $- 2$ .

$4 + b = - 7$

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

Subtract $4$ from both sides of the equation.

$b = - 7 - 4$

Subtract $4$ from $- 7$ .

$b = - 11$

Step 3

List the slope and y-intercept.

Slope: $- \frac{2}{5}$

y-intercept: $(0, - 11)$

Step 4

Find the Slope and y-intercept (-10,-7) , (-5,-9)

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