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

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

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

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $1$ .

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

Simplify the denominator.

Multiply $- 1$ by $0$ .

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

Add $- 5$ and $0$ .

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

Dividing two negative values results in a positive value.

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

Use the slope $\frac{4}{5}$ and a given point $(0, 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (5) = \frac{4}{5} \cdot (x - (0))$

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

$y - 5 = \frac{4}{5} \cdot (x + 0)$

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

Solve for $y$ .

Simplify $\frac{4}{5} \cdot (x + 0)$ .

Add $x$ and $0$ .

$y - 5 = \frac{4}{5} \cdot x$

Combine $\frac{4}{5}$ and $x$ .

$y - 5 = \frac{4 x}{5}$

Add $5$ to both sides of the equation.

$y = \frac{4 x}{5} + 5$

Reorder terms.

$y = \frac{4}{5} x + 5$

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

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