Find the Equation Using Slope-Intercept Form m=-4 , (3,5)

$m = - 4$ , $(3, 5)$

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.

$y = (- 4) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 4) \cdot (3) + b$

Substitute the value of $y$ into the equation.

$5 = (- 4) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $(- 4) \cdot (3) + b = 5$ .

$(- 4) \cdot (3) + b = 5$

Multiply $- 4$ by $3$ .

$- 12 + b = 5$

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

Add $12$ to both sides of the equation.

$b = 5 + 12$

Add $5$ and $12$ .

$b = 17$

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.

$y = - 4 x + 17$

Step 3