Find the Slope and y-intercept (-2,7) , (3,2)

$(- 2, 7)$ , $(3, 2)$

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.

$m = \frac{2 - (7)}{3 - (- 2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $7$ .

$m = \frac{2 - 7}{3 - (- 2)}$

Subtract $7$ from $2$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 2$ .

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

Add $3$ and $2$ .

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

Divide $- 5$ by $5$ .

$m = - 1$

Find the value of the y-intercept.

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

$y = (- 1) \cdot x + b$

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

$y = (- 1) \cdot (- 2) + b$

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

$7 = (- 1) \cdot (- 2) + b$

Rewrite the equation as $(- 1) \cdot (- 2) + b = 7$ .

$(- 1) \cdot (- 2) + b = 7$

Multiply $- 1$ by $- 2$ .

$2 + b = 7$

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

Subtract $2$ from both sides of the equation.

$b = 7 - 2$

Subtract $2$ from $7$ .

$b = 5$

List the slope and y-intercept.

Slope: $- 1$

y-intercept: $(0, 5)$

Find the Slope and y-intercept (-2,7) , (3,2)

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