Find the Slope and y-intercept (-4,24) , (7,-53)

$(- 4, 24)$ , $(7, - 53)$

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.

$m = \frac{- 53 - (24)}{7 - (- 4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $24$ .

$m = \frac{- 53 - 24}{7 - (- 4)}$

Subtract $24$ from $- 53$ .

$m = \frac{- 77}{7 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{- 77}{7 + 4}$

Add $7$ and $4$ .

$m = \frac{- 77}{11}$

Divide $- 77$ by $11$ .

$m = - 7$

Step 2

Find the value of the y-intercept.

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

$y = (- 7) \cdot x + b$

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

$y = (- 7) \cdot (- 4) + b$

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

$24 = (- 7) \cdot (- 4) + b$

Rewrite the equation as $(- 7) \cdot (- 4) + b = 24$ .

$(- 7) \cdot (- 4) + b = 24$

Multiply $- 7$ by $- 4$ .

$28 + b = 24$

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

Subtract $28$ from both sides of the equation.

$b = 24 - 28$

Subtract $28$ from $24$ .

$b = - 4$

Step 3

List the slope and y-intercept.

Slope: $- 7$

y-intercept: $(0, - 4)$

Step 4

Find the Slope and y-intercept (-4,24) , (7,-53)

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