Write in Slope-Intercept Form (6,-2) and (12,1)

$(6, - 2)$ and $(12, 1)$

Find the slope of the line between $(6, - 2)$ and $(12, 1)$ 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.

$m = \frac{1 - (- 2)}{12 - (6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 2$ .

$m = \frac{1 + 2}{12 - (6)}$

Add $1$ and $2$ .

$m = \frac{3}{12 - (6)}$

Simplify the denominator.

Multiply $- 1$ by $6$ .

$m = \frac{3}{12 - 6}$

Subtract $6$ from $12$ .

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

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

$m = \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$m = \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

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

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

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

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

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

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

Solve for $y$ .

Simplify $\frac{1}{2} \cdot (x - 6)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

$y + 2 = \frac{1}{2} x + \frac{1}{2} \cdot - 6$

Combine $\frac{1}{2}$ and $x$ .

$y + 2 = \frac{x}{2} + \frac{1}{2} \cdot - 6$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$y + 2 = \frac{x}{2} + \frac{1}{2} \cdot (2 (- 3))$

Cancel the common factor.

$y + 2 = \frac{x}{2} + \frac{1}{2} \cdot (2 \cdot - 3)$

Rewrite the expression.

$y + 2 = \frac{x}{2} - 3$

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

Subtract $2$ from both sides of the equation.

$y = \frac{x}{2} - 3 - 2$

Subtract $2$ from $- 3$ .

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

Reorder terms.

$y = \frac{1}{2} x - 5$

Write in Slope-Intercept Form (6,-2) and (12,1)

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