Write in Slope-Intercept Form (-1,-5) and (2,2)

$(- 1, - 5)$ and $(2, 2)$

Find the slope of the line between $(- 1, - 5)$ and $(2, 2)$ 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.

$m = \frac{2 - (- 5)}{2 - (- 1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 5$ .

$m = \frac{2 + 5}{2 - (- 1)}$

Add $2$ and $5$ .

$m = \frac{7}{2 - (- 1)}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$m = \frac{7}{2 + 1}$

Add $2$ and $1$ .

$m = \frac{7}{3}$

Use the slope $\frac{7}{3}$ and a given point $(- 1, - 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 5) = \frac{7}{3} \cdot (x - (- 1))$

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

$y + 5 = \frac{7}{3} \cdot (x + 1)$

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

Solve for $y$ .

Simplify $\frac{7}{3} \cdot (x + 1)$ .

Rewrite.

$y + 5 = 0 + 0 + \frac{7}{3} \cdot (x + 1)$

Simplify by adding zeros.

$y + 5 = \frac{7}{3} \cdot (x + 1)$

Apply the distributive property.

$y + 5 = \frac{7}{3} x + \frac{7}{3} \cdot 1$

Combine $\frac{7}{3}$ and $x$ .

$y + 5 = \frac{7 x}{3} + \frac{7}{3} \cdot 1$

Multiply $\frac{7}{3}$ by $1$ .

$y + 5 = \frac{7 x}{3} + \frac{7}{3}$

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

Subtract $5$ from both sides of the equation.

$y = \frac{7 x}{3} + \frac{7}{3} - 5$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{7 x}{3} + \frac{7}{3} - 5 \cdot \frac{3}{3}$

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

$y = \frac{7 x}{3} + \frac{7}{3} + \frac{- 5 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{7 x}{3} + \frac{7 - 5 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 5$ by $3$ .

$y = \frac{7 x}{3} + \frac{7 - 15}{3}$

Subtract $15$ from $7$ .

$y = \frac{7 x}{3} + \frac{- 8}{3}$

Move the negative in front of the fraction.

$y = \frac{7 x}{3} - \frac{8}{3}$

Reorder terms.

$y = \frac{7}{3} x - \frac{8}{3}$

Write in Slope-Intercept Form (-1,-5) and (2,2)

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