Find the Equation Using Point-Slope Formula m=5 , (3,-12)

$m = 5$ , $(3, - 12)$

Step 1

Use the slope $5$ and a given point $(3, - 12)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 12) = 5 \cdot (x - (3))$

Step 2

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

$y + 12 = 5 \cdot (x - 3)$

Step 3

Solve for $y$ .

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

Rewrite.

$y + 12 = 0 + 0 + 5 \cdot (x - 3)$

Simplify by adding zeros.

$y + 12 = 5 \cdot (x - 3)$

Apply the distributive property.

$y + 12 = 5 x + 5 \cdot - 3$

Multiply $5$ by $- 3$ .

$y + 12 = 5 x - 15$

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

Subtract $12$ from both sides of the equation.

$y = 5 x - 15 - 12$

Subtract $12$ from $- 15$ .

$y = 5 x - 27$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = 5 x - 27$

Point-slope form:

$y + 12 = 5 \cdot (x - 3)$

Step 5

Find the Equation Using Point-Slope Formula m=5 , (3,-12)

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