Find the Equation Using Point-Slope Formula (3,6) and (5,-8)

$(3, 6)$ and $(5, - 8)$

Find the slope of the line between $(3, 6)$ and $(5, - 8)$ 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.

$m = \frac{- 8 - (6)}{5 - (3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $6$ .

$m = \frac{- 8 - 6}{5 - (3)}$

Subtract $6$ from $- 8$ .

$m = \frac{- 14}{5 - (3)}$

Simplify the denominator.

Multiply $- 1$ by $3$ .

$m = \frac{- 14}{5 - 3}$

Subtract $3$ from $5$ .

$m = \frac{- 14}{2}$

Divide $- 14$ by $2$ .

$m = - 7$

Use the slope $- 7$ and a given point $(3, 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (6) = - 7 \cdot (x - (3))$

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

$y - 6 = - 7 \cdot (x - 3)$

Solve for $y$ .

Simplify $- 7 \cdot (x - 3)$ .

Rewrite.

$y - 6 = 0 + 0 - 7 \cdot (x - 3)$

Simplify by adding zeros.

$y - 6 = - 7 \cdot (x - 3)$

Apply the distributive property.

$y - 6 = - 7 x - 7 \cdot - 3$

Multiply $- 7$ by $- 3$ .

$y - 6 = - 7 x + 21$

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

Add $6$ to both sides of the equation.

$y = - 7 x + 21 + 6$

Add $21$ and $6$ .

$y = - 7 x + 27$

List the equation in different forms.

Slope-intercept form:

$y = - 7 x + 27$

Point-slope form:

$y - 6 = - 7 \cdot (x - 3)$

Find the Equation Using Point-Slope Formula (3,6) and (5,-8)

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