Find the Slope and y-intercept (5,21) , (-5,-29)

$(5, 21)$ , $(- 5, - 29)$

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.

$m = \frac{- 29 - (21)}{- 5 - (5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $21$ .

$m = \frac{- 29 - 21}{- 5 - (5)}$

Subtract $21$ from $- 29$ .

$m = \frac{- 50}{- 5 - (5)}$

Simplify the denominator.

Multiply $- 1$ by $5$ .

$m = \frac{- 50}{- 5 - 5}$

Subtract $5$ from $- 5$ .

$m = \frac{- 50}{- 10}$

Divide $- 50$ by $- 10$ .

$m = 5$

Find the value of the y-intercept.

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

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

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

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

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

$21 = (5) \cdot (5) + b$

Rewrite the equation as $(5) \cdot (5) + b = 21$ .

$(5) \cdot (5) + b = 21$

Multiply $5$ by $5$ .

$25 + b = 21$

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

Subtract $25$ from both sides of the equation.

$b = 21 - 25$

Subtract $25$ from $21$ .

$b = - 4$

List the slope and y-intercept.

Slope: $5$

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

Find the Slope and y-intercept (5,21) , (-5,-29)

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