Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-8,1) and has a slope of -3/4 ?

What is the equation of the line that passes through the point $(- 8, 1)$ and has a slope of $- \frac{3}{4}$ ?

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.

$y = (- \frac{3}{4}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{3}{4}) \cdot (- 8) + b$

Substitute the value of $y$ into the equation.

$1 = (- \frac{3}{4}) \cdot (- 8) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{3}{4} \cdot - 8 + b = 1$ .

$- \frac{3}{4} \cdot - 8 + b = 1$

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot - 8 + b = 1$

Factor $4$ out of $- 8$ .

$\frac{- 3}{4} \cdot (4 (- 2)) + b = 1$

Cancel the common factor.

$\frac{- 3}{4} \cdot (4 \cdot - 2) + b = 1$

Rewrite the expression.

$- 3 \cdot - 2 + b = 1$

Multiply $- 3$ by $- 2$ .

$6 + b = 1$

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

Subtract $6$ from both sides of the equation.

$b = 1 - 6$

Subtract $6$ from $1$ .

$b = - 5$

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.

$y = - \frac{3}{4} x - 5$

Step 3