Find the Equation Using Point-Slope Formula through: (-2,5) , slope=-4

through: $(- 2, 5)$ , $s l o p e = - 4$

Step 1

Use the slope $- 4$ and a given point $(- 2, 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (5) = - 4 \cdot (x - (- 2))$

Step 2

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

$y - 5 = - 4 \cdot (x + 2)$

Step 3

Solve for $y$ .

Simplify $- 4 \cdot (x + 2)$ .

Rewrite.

$y - 5 = 0 + 0 - 4 \cdot (x + 2)$

Simplify by adding zeros.

$y - 5 = - 4 \cdot (x + 2)$

Apply the distributive property.

$y - 5 = - 4 x - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$y - 5 = - 4 x - 8$

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

Add $5$ to both sides of the equation.

$y = - 4 x - 8 + 5$

Add $- 8$ and $5$ .

$y = - 4 x - 3$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - 4 x - 3$

Point-slope form:

$y - 5 = - 4 \cdot (x + 2)$

Step 5

Find the Equation Using Point-Slope Formula through: (-2,5) , slope=-4

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