Find the Slope and y-intercept (2,-5) , (-4,1)

$(2, - 5)$ , $(- 4, 1)$

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.

$m = \frac{1 - (- 5)}{- 4 - (2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 5$ .

$m = \frac{1 + 5}{- 4 - (2)}$

Add $1$ and $5$ .

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

Simplify the denominator.

Multiply $- 1$ by $2$ .

$m = \frac{6}{- 4 - 2}$

Subtract $2$ from $- 4$ .

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

Divide $6$ by $- 6$ .

$m = - 1$

Step 2

Find the value of the y-intercept.

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

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

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, $y = m x + b$ .

$- 5 = (- 1) \cdot (2) + b$

Rewrite the equation as $(- 1) \cdot (2) + b = - 5$ .

$(- 1) \cdot (2) + b = - 5$

Multiply $- 1$ by $2$ .

$- 2 + b = - 5$

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

Add $2$ to both sides of the equation.

$b = - 5 + 2$

Add $- 5$ and $2$ .

$b = - 3$

Step 3

List the slope and y-intercept.

Slope: $- 1$

y-intercept: $(0, - 3)$

Step 4

Find the Slope and y-intercept (2,-5) , (-4,1)

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