Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-4,-8) and has a slope of 4 ?

What is the equation of the line that passes through the point $(- 4, - 8)$ and has a slope of $4$ ?

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.

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

Substitute the value of $y$ into the equation.

$- 8 = (4) \cdot (- 4) + b$

Find the value of $b$ .

Rewrite the equation as $(4) \cdot (- 4) + b = - 8$ .

$(4) \cdot (- 4) + b = - 8$

Multiply $4$ by $- 4$ .

$- 16 + b = - 8$

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

Add $16$ to both sides of the equation.

$b = - 8 + 16$

Add $- 8$ and $16$ .

$b = 8$

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.

$y = 4 x + 8$

Step 3