Find the Slope and y-intercept (-4,2) , (6,-3)

$(- 4, 2)$ , $(6, - 3)$

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.

$m = \frac{- 3 - (2)}{6 - (- 4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $2$ .

$m = \frac{- 3 - 2}{6 - (- 4)}$

Subtract $2$ from $- 3$ .

$m = \frac{- 5}{6 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{- 5}{6 + 4}$

Add $6$ and $4$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 5$ and $10$ .

Factor $5$ out of $- 5$ .

$m = \frac{5 (- 1)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$m = \frac{5 \cdot - 1}{5 \cdot 2}$

Cancel the common factor.

$m = \frac{5 \cdot - 1}{5 \cdot 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 2

Find the value of the y-intercept.

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

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

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

$y = (- \frac{1}{2}) \cdot (- 4) + b$

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

$2 = (- \frac{1}{2}) \cdot (- 4) + b$

Rewrite the equation as $(- \frac{1}{2}) \cdot (- 4) + b = 2$ .

$(- \frac{1}{2}) \cdot (- 4) + b = 2$

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot - 4 + b = 2$

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 1 \cdot - 2 + b = 2$

Multiply $- 1$ by $- 2$ .

$2 + b = 2$

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

Subtract $2$ from both sides of the equation.

$b = 2 - 2$

Subtract $2$ from $2$ .

$b = 0$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{2}$

y-intercept: $(0, 0)$

Step 4

Find the Slope and y-intercept (-4,2) , (6,-3)

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