Find the Slope and y-intercept (5,35) , (-6,-31)

$(5, 35)$ , $(- 6, - 31)$

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.

$m = \frac{- 31 - (35)}{- 6 - (5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $35$ .

$m = \frac{- 31 - 35}{- 6 - (5)}$

Subtract $35$ from $- 31$ .

$m = \frac{- 66}{- 6 - (5)}$

Simplify the denominator.

Multiply $- 1$ by $5$ .

$m = \frac{- 66}{- 6 - 5}$

Subtract $5$ from $- 6$ .

$m = \frac{- 66}{- 11}$

Divide $- 66$ by $- 11$ .

$m = 6$

Step 2

Find the value of the y-intercept.

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

$y = (6) \cdot x + b$

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

$y = (6) \cdot (5) + b$

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

$35 = (6) \cdot (5) + b$

Rewrite the equation as $(6) \cdot (5) + b = 35$ .

$(6) \cdot (5) + b = 35$

Multiply $6$ by $5$ .

$30 + b = 35$

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

Subtract $30$ from both sides of the equation.

$b = 35 - 30$

Subtract $30$ from $35$ .

$b = 5$

Step 3

List the slope and y-intercept.

Slope: $6$

y-intercept: $(0, 5)$

Step 4

Find the Slope and y-intercept (5,35) , (-6,-31)

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