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 $- \frac{3}{4}$ ?

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.

Add $6$ to both sides of the equation.

$b = 1 + 6$

Add $1$ and $6$ .

$b = 7$

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.

$y = - \frac{3}{4} x + 7$