Find the Equation Using Slope-Intercept Form (3,-8) and 7(-2)

$(3, - 8)$ and $7 (- 2)$

Multiply $7$ by $- 2$ .

$m = - 14$

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.

$y = (- 14) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 14) \cdot (3) + b$

Substitute the value of $y$ into the equation.

$- 8 = (- 14) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $(- 14) \cdot (3) + b = - 8$ .

$(- 14) \cdot (3) + b = - 8$

Multiply $- 14$ by $3$ .

$- 42 + b = - 8$

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

Add $42$ to both sides of the equation.

$b = - 8 + 42$

Add $- 8$ and $42$ .

$b = 34$

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.

$y = - 14 x + 34$