Find the Equation Using Slope-Intercept Form m=-9 , (5,7)

$m = - 9$ , $(5, 7)$

Step 1

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.

$y = (- 9) \cdot x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$7 = (- 9) \cdot (5) + b$

Find the value of $b$ .

Rewrite the equation as $(- 9) \cdot (5) + b = 7$ .

$(- 9) \cdot (5) + b = 7$

Multiply $- 9$ by $5$ .

$- 45 + b = 7$

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

Add $45$ to both sides of the equation.

$b = 7 + 45$

Add $7$ and $45$ .

$b = 52$

Step 2

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.

$y = - 9 x + 52$

Step 3