Find the Equation Using Slope-Intercept Form (3,-9) , m=-5

$(3, - 9)$ , $m = - 5$

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$- 9 = (- 5) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $(- 5) \cdot (3) + b = - 9$ .

$(- 5) \cdot (3) + b = - 9$

Multiply $- 5$ by $3$ .

$- 15 + b = - 9$

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

Add $15$ to both sides of the equation.

$b = - 9 + 15$

Add $- 9$ and $15$ .

$b = 6$

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.

$y = - 5 x + 6$