Write in Slope-Intercept Form (5,0) and (-1,4)

$(5, 0)$ and $(- 1, 4)$

Find the slope of the line between $(5, 0)$ and $(- 1, 4)$ 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.

$m = \frac{4 - (0)}{- 1 - (5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{4 + 0}{- 1 - (5)}$

Add $4$ and $0$ .

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

Simplify the denominator.

Multiply $- 1$ by $5$ .

$m = \frac{4}{- 1 - 5}$

Subtract $5$ from $- 1$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ and $- 6$ .

Factor $2$ out of $4$ .

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

Cancel the common factors.

Factor $2$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Use the slope $- \frac{2}{3}$ and a given point $(5, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{2}{3} \cdot (x - (5))$

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

$y + 0 = - \frac{2}{3} \cdot (x - 5)$

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

Solve for $y$ .

Add $y$ and $0$ .

$y = - \frac{2}{3} \cdot (x - 5)$

Simplify $- \frac{2}{3} \cdot (x - 5)$ .

Apply the distributive property.

$y = - \frac{2}{3} x - \frac{2}{3} \cdot - 5$

Combine $x$ and $\frac{2}{3}$ .

$y = - \frac{x \cdot 2}{3} - \frac{2}{3} \cdot - 5$

Multiply $- \frac{2}{3} \cdot - 5$ .

Multiply $- 5$ by $- 1$ .

$y = - \frac{x \cdot 2}{3} + 5 (\frac{2}{3})$

Combine $5$ and $\frac{2}{3}$ .

$y = - \frac{x \cdot 2}{3} + \frac{5 \cdot 2}{3}$

Multiply $5$ by $2$ .

$y = - \frac{x \cdot 2}{3} + \frac{10}{3}$

Move $2$ to the left of $x$ .

$y = - \frac{2 x}{3} + \frac{10}{3}$

Reorder terms.

$y = - (\frac{2}{3} x) + \frac{10}{3}$

Remove parentheses.

$y = - \frac{2}{3} x + \frac{10}{3}$

Write in Slope-Intercept Form (5,0) and (-1,4)

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