Find the Equation Using Slope-Intercept Form (-7,2) , m=3

$(- 7, 2)$ , $m = 3$

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.

$y = (3) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (3) \cdot (- 7) + b$

Substitute the value of $y$ into the equation.

$2 = (3) \cdot (- 7) + b$

Find the value of $b$ .

Rewrite the equation as $(3) \cdot (- 7) + b = 2$ .

$(3) \cdot (- 7) + b = 2$

Multiply $3$ by $- 7$ .

$- 21 + b = 2$

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

Add $21$ to both sides of the equation.

$b = 2 + 21$

Add $2$ and $21$ .

$b = 23$

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.

$y = 3 x + 23$