Write in Slope-Intercept Form (-4,13) and (-2,6)

$(- 4, 13)$ and $(- 2, 6)$

Step 1

Find the slope of the line between $(- 4, 13)$ and $(- 2, 6)$ 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.

$m = \frac{6 - (13)}{- 2 - (- 4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $13$ .

$m = \frac{6 - 13}{- 2 - (- 4)}$

Subtract $13$ from $6$ .

$m = \frac{- 7}{- 2 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{- 7}{- 2 + 4}$

Add $- 2$ and $4$ .

$m = \frac{- 7}{2}$

Move the negative in front of the fraction.

$m = - \frac{7}{2}$

Step 2

Use the slope $- \frac{7}{2}$ and a given point $(- 4, 13)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (13) = - \frac{7}{2} \cdot (x - (- 4))$

Step 3

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

$y - 13 = - \frac{7}{2} \cdot (x + 4)$

Step 4

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

Solve for $y$ .

Simplify $- \frac{7}{2} \cdot (x + 4)$ .

Rewrite.

$y - 13 = 0 + 0 - \frac{7}{2} \cdot (x + 4)$

Simplify terms.

Apply the distributive property.

$y - 13 = - \frac{7}{2} x - \frac{7}{2} \cdot 4$

Combine $x$ and $\frac{7}{2}$ .

$y - 13 = - \frac{x \cdot 7}{2} - \frac{7}{2} \cdot 4$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$y - 13 = - \frac{x \cdot 7}{2} + \frac{- 7}{2} \cdot 4$

Factor $2$ out of $4$ .

$y - 13 = - \frac{x \cdot 7}{2} + \frac{- 7}{2} \cdot (2 (2))$

Cancel the common factor.

$y - 13 = - \frac{x \cdot 7}{2} + \frac{- 7}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$y - 13 = - \frac{x \cdot 7}{2} - 7 \cdot 2$

Multiply $- 7$ by $2$ .

$y - 13 = - \frac{x \cdot 7}{2} - 14$

Move $7$ to the left of $x$ .

$y - 13 = - \frac{7 x}{2} - 14$

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

Add $13$ to both sides of the equation.

$y = - \frac{7 x}{2} - 14 + 13$

Add $- 14$ and $13$ .

$y = - \frac{7 x}{2} - 1$

Reorder terms.

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

Remove parentheses.

$y = - \frac{7}{2} x - 1$

Step 5

Write in Slope-Intercept Form (-4,13) and (-2,6)

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