Find the Slope and y-intercept (-2,-3) , (4,-5)

$(- 2, - 3)$ , $(4, - 5)$

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.

$m = \frac{- 5 - (- 3)}{4 - (- 2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 3$ .

$m = \frac{- 5 + 3}{4 - (- 2)}$

Add $- 5$ and $3$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 2$ .

$m = \frac{- 2}{4 + 2}$

Add $4$ and $2$ .

$m = \frac{- 2}{6}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

$m = \frac{2 (- 1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$m = \frac{2 \cdot - 1}{2 \cdot 3}$

Cancel the common factor.

$m = \frac{2 \cdot - 1}{2 \cdot 3}$

Rewrite the expression.

$m = \frac{- 1}{3}$

Move the negative in front of the fraction.

$m = - \frac{1}{3}$

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{1}{3}) \cdot x + b$

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

$y = (- \frac{1}{3}) \cdot (- 2) + b$

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

$- 3 = (- \frac{1}{3}) \cdot (- 2) + b$

Rewrite the equation as $(- \frac{1}{3}) \cdot (- 2) + b = - 3$ .

$(- \frac{1}{3}) \cdot (- 2) + b = - 3$

Multiply $(- \frac{1}{3}) (- 2)$ .

Multiply $- 2$ by $- 1$ .

$2 (\frac{1}{3}) + b = - 3$

Combine $2$ and $\frac{1}{3}$ .

$\frac{2}{3} + b = - 3$

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

Subtract $\frac{2}{3}$ from both sides of the equation.

$b = - 3 - \frac{2}{3}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - 3 \cdot \frac{3}{3} - \frac{2}{3}$

Combine $- 3$ and $\frac{3}{3}$ .

$b = \frac{- 3 \cdot 3}{3} - \frac{2}{3}$

Combine the numerators over the common denominator.

$b = \frac{- 3 \cdot 3 - 2}{3}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$b = \frac{- 9 - 2}{3}$

Subtract $2$ from $- 9$ .

$b = \frac{- 11}{3}$

Move the negative in front of the fraction.

$b = - \frac{11}{3}$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{3}$

y-intercept: $(0, - \frac{11}{3})$

Step 4

Find the Slope and y-intercept (-2,-3) , (4,-5)

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