Find the Equation Using Point-Slope Formula (-5,-3) , m=-2

$(- 5, - 3)$ , $m = - 2$

Step 1

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

$y - (- 3) = - 2 \cdot (x - (- 5))$

Step 2

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

$y + 3 = - 2 \cdot (x + 5)$

Step 3

Solve for $y$ .

Simplify $- 2 \cdot (x + 5)$ .

Rewrite.

$y + 3 = 0 + 0 - 2 \cdot (x + 5)$

Simplify by adding zeros.

$y + 3 = - 2 \cdot (x + 5)$

Apply the distributive property.

$y + 3 = - 2 x - 2 \cdot 5$

Multiply $- 2$ by $5$ .

$y + 3 = - 2 x - 10$

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

Subtract $3$ from both sides of the equation.

$y = - 2 x - 10 - 3$

Subtract $3$ from $- 10$ .

$y = - 2 x - 13$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - 2 x - 13$

Point-slope form:

$y + 3 = - 2 \cdot (x + 5)$

Step 5

Find the Equation Using Point-Slope Formula (-5,-3) , m=-2

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