Write in y=mx+b Form (6,-6) and (8,8)

$(6, - 6)$ and $(8, 8)$

Step 1

Find the slope of the line between $(6, - 6)$ and $(8, 8)$ 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.

$m = \frac{8 - (- 6)}{8 - (6)}$

Simplify.

Cancel the common factor of $8 - (- 6)$ and $8 - (6)$ .

Rewrite $8$ as $- 1 (- 8)$ .

$m = \frac{8 - (- 6)}{- 1 \cdot - 8 - (6)}$

Factor $- 1$ out of $- 1 (- 8) - (6)$ .

$m = \frac{8 - (- 6)}{- 1 (- 8 + 6)}$

Reorder terms.

$m = \frac{8 - 6 \cdot - 1}{- 1 (- 8 + 6)}$

Factor $2$ out of $8$ .

$m = \frac{2 (4) - 6 \cdot - 1}{- 1 (- 8 + 6)}$

Factor $2$ out of $- 6 \cdot - 1$ .

$m = \frac{2 (4) + 2 (- 3 \cdot - 1)}{- 1 (- 8 + 6)}$

Factor $2$ out of $2 (4) + 2 (- 3 \cdot - 1)$ .

$m = \frac{2 (4 - 3 \cdot - 1)}{- 1 (- 8 + 6)}$

Cancel the common factors.

Factor $2$ out of $- 1 (- 8 + 6)$ .

$m = \frac{2 (4 - 3 \cdot - 1)}{2 (- 1 (- 4 + 3))}$

Cancel the common factor.

$m = \frac{2 (4 - 3 \cdot - 1)}{2 (- 1 (- 4 + 3))}$

Rewrite the expression.

$m = \frac{4 - 3 \cdot - 1}{- 1 (- 4 + 3)}$

Simplify the numerator.

Multiply $- 3$ by $- 1$ .

$m = \frac{4 + 3}{- 1 (- 4 + 3)}$

Add $4$ and $3$ .

$m = \frac{7}{- 1 (- 4 + 3)}$

Simplify the expression.

Add $- 4$ and $3$ .

$m = \frac{7}{- 1 \cdot - 1}$

Multiply $- 1$ by $- 1$ .

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

Divide $7$ by $1$ .

$m = 7$

Step 2

Use the slope $7$ and a given point $(6, - 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 6) = 7 \cdot (x - (6))$

Step 3

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

$y + 6 = 7 \cdot (x - 6)$

Step 4

Solve for $y$ .

Simplify $7 \cdot (x - 6)$ .

Rewrite.

$y + 6 = 0 + 0 + 7 \cdot (x - 6)$

Simplify by adding zeros.

$y + 6 = 7 \cdot (x - 6)$

Apply the distributive property.

$y + 6 = 7 x + 7 \cdot - 6$

Multiply $7$ by $- 6$ .

$y + 6 = 7 x - 42$

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

Subtract $6$ from both sides of the equation.

$y = 7 x - 42 - 6$

Subtract $6$ from $- 42$ .

$y = 7 x - 48$

Step 5

Write in y=mx+b Form (6,-6) and (8,8)

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