Find the Equation Using Slope-Intercept Form m=-7 , (3,6)

$m = - 7$ , $(3, 6)$

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$6 = (- 7) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $(- 7) \cdot (3) + b = 6$ .

$(- 7) \cdot (3) + b = 6$

Multiply $- 7$ by $3$ .

$- 21 + b = 6$

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

Add $21$ to both sides of the equation.

$b = 6 + 21$

Add $6$ and $21$ .

$b = 27$

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.

$y = - 7 x + 27$