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 -1/4 ?

What is the equation of the line that passes through the point $(- 4, 8)$ and has a slope of $- \frac{1}{4}$ ?

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.

$y = (- \frac{1}{4}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{1}{4}) \cdot (- 4) + b$

Substitute the value of $y$ into the equation.

$8 = (- \frac{1}{4}) \cdot (- 4) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{1}{4} \cdot - 4 + b = 8$ .

$- \frac{1}{4} \cdot - 4 + b = 8$

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} \cdot - 4 + b = 8$

Factor $4$ out of $- 4$ .

$\frac{- 1}{4} \cdot (4 (- 1)) + b = 8$

Cancel the common factor.

$\frac{- 1}{4} \cdot (4 \cdot - 1) + b = 8$

Rewrite the expression.

$- 1 \cdot - 1 + b = 8$

Multiply $- 1$ by $- 1$ .

$1 + b = 8$

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

Subtract $1$ from both sides of the equation.

$b = 8 - 1$

Subtract $1$ from $8$ .

$b = 7$

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.

$y = - \frac{1}{4} x + 7$

Step 3