Write in Slope-Intercept Form (6,-1) , (3,-7)

$(6, - 1)$ , $(3, - 7)$

Step 1

Find the slope of the line between $(6, - 1)$ and $(3, - 7)$ 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.

$m = \frac{- 7 - (- 1)}{3 - (6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{- 7 + 1}{3 - (6)}$

Add $- 7$ and $1$ .

$m = \frac{- 6}{3 - (6)}$

Simplify the denominator.

Multiply $- 1$ by $6$ .

$m = \frac{- 6}{3 - 6}$

Subtract $6$ from $3$ .

$m = \frac{- 6}{- 3}$

Divide $- 6$ by $- 3$ .

$m = 2$

Step 2

Use the slope $2$ and a given point $(6, - 1)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 1) = 2 \cdot (x - (6))$

Step 3

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

$y + 1 = 2 \cdot (x - 6)$

Step 4

Solve for $y$ .

Simplify $2 \cdot (x - 6)$ .

Rewrite.

$y + 1 = 0 + 0 + 2 \cdot (x - 6)$

Simplify by adding zeros.

$y + 1 = 2 \cdot (x - 6)$

Apply the distributive property.

$y + 1 = 2 x + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$y + 1 = 2 x - 12$

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

Subtract $1$ from both sides of the equation.

$y = 2 x - 12 - 1$

Subtract $1$ from $- 12$ .

$y = 2 x - 13$

Step 5

Write in Slope-Intercept Form (6,-1) , (3,-7)

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