Find the Equation Using Point-Slope Formula (5,-8) ; m=-3

$(5, - 8)$ ; $m = - 3$

Step 1

Use the slope $- 3$ and a given point $(5, - 8)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 8) = - 3 \cdot (x - (5))$

Step 2

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

$y + 8 = - 3 \cdot (x - 5)$

Step 3

Solve for $y$ .

Simplify $- 3 \cdot (x - 5)$ .

Rewrite.

$y + 8 = 0 + 0 - 3 \cdot (x - 5)$

Simplify by adding zeros.

$y + 8 = - 3 \cdot (x - 5)$

Apply the distributive property.

$y + 8 = - 3 x - 3 \cdot - 5$

Multiply $- 3$ by $- 5$ .

$y + 8 = - 3 x + 15$

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

Subtract $8$ from both sides of the equation.

$y = - 3 x + 15 - 8$

Subtract $8$ from $15$ .

$y = - 3 x + 7$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - 3 x + 7$

Point-slope form:

$y + 8 = - 3 \cdot (x - 5)$

Step 5

Find the Equation Using Point-Slope Formula (5,-8) ; m=-3

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