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

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

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.

$y = (- 6) \cdot x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Multiply $- 6$ by $3$ .

$- 18 + b = 7$

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

Add $18$ to both sides of the equation.

$b = 7 + 18$

Add $7$ and $18$ .

$b = 25$

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.

$y = - 6 x + 25$