Write in Slope-Intercept Form (-5,19) and (5,13)

$(- 5, 19)$ and $(5, 13)$

Find the slope of the line between $(- 5, 19)$ and $(5, 13)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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.

$m = \frac{13 - (19)}{5 - (- 5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $19$ .

$m = \frac{13 - 19}{5 - (- 5)}$

Subtract $19$ from $13$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 5$ .

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

Add $5$ and $5$ .

$m = \frac{- 6}{10}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 6$ and $10$ .

Factor $2$ out of $- 6$ .

$m = \frac{2 (- 3)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Use the slope $- \frac{3}{5}$ and a given point $(- 5, 19)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (19) = - \frac{3}{5} \cdot (x - (- 5))$

Simplify the equation and keep it in point-slope form.

$y - 19 = - \frac{3}{5} \cdot (x + 5)$

Write the equation in $y = m x + b$ form.

Solve for $y$ .

Simplify $- \frac{3}{5} \cdot (x + 5)$ .

Rewrite.

$y - 19 = 0 + 0 - \frac{3}{5} \cdot (x + 5)$

Simplify terms.

Apply the distributive property.

$y - 19 = - \frac{3}{5} x - \frac{3}{5} \cdot 5$

Combine $x$ and $\frac{3}{5}$ .

$y - 19 = - \frac{x \cdot 3}{5} - \frac{3}{5} \cdot 5$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$y - 19 = - \frac{x \cdot 3}{5} + \frac{- 3}{5} \cdot 5$

Cancel the common factor.

$y - 19 = - \frac{x \cdot 3}{5} + \frac{- 3}{5} \cdot 5$

Rewrite the expression.

$y - 19 = - \frac{x \cdot 3}{5} - 3$

Move $3$ to the left of $x$ .

$y - 19 = - \frac{3 x}{5} - 3$

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

Add $19$ to both sides of the equation.

$y = - \frac{3 x}{5} - 3 + 19$

Add $- 3$ and $19$ .

$y = - \frac{3 x}{5} + 16$

Reorder terms.

$y = - (\frac{3}{5} x) + 16$

Remove parentheses.

$y = - \frac{3}{5} x + 16$

Write in Slope-Intercept Form (-5,19) and (5,13)

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