Write in Slope-Intercept Form (-2,0) and (0,5)

$(- 2, 0)$ and $(0, 5)$

Step 1

Find the slope of the line between $(- 2, 0)$ and $(0, 5)$ 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.

$m = \frac{5 - (0)}{0 - (- 2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{5 + 0}{0 - (- 2)}$

Add $5$ and $0$ .

$m = \frac{5}{0 - (- 2)}$

Simplify the denominator.

Multiply $- 1$ by $- 2$ .

$m = \frac{5}{0 + 2}$

Add $0$ and $2$ .

$m = \frac{5}{2}$

Step 2

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

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

Step 3

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

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

Step 4

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

Solve for $y$ .

Add $y$ and $0$ .

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

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

Apply the distributive property.

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{5 x}{2} + 5$

Reorder terms.

$y = \frac{5}{2} x + 5$

Step 5

Write in Slope-Intercept Form (-2,0) and (0,5)

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