Find the Equation Using Slope-Intercept Form (-5,-3) , m=-2

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

Step 1

Find the value of $b$ using the formula for the equation of a line.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (- 2) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 2) \cdot (- 5) + b$

Substitute the value of $y$ into the equation.

$- 3 = (- 2) \cdot (- 5) + b$

Find the value of $b$ .

Rewrite the equation as $(- 2) \cdot (- 5) + b = - 3$ .

$(- 2) \cdot (- 5) + b = - 3$

Multiply $- 2$ by $- 5$ .

$10 + b = - 3$

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

Subtract $10$ from both sides of the equation.

$b = - 3 - 10$

Subtract $10$ from $- 3$ .

$b = - 13$

Step 2

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - 2 x - 13$

Step 3