Find the Equation with a Point and Slope m=3/4 , (5,-8)

$m = \frac{3}{4}$ , $(5, - 8)$

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.

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

Substitute the value of $x$ into the equation.

$y = (\frac{3}{4}) \cdot (5) + b$

Substitute the value of $y$ into the equation.

$- 8 = (\frac{3}{4}) \cdot (5) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{3}{4} \cdot 5 + b = - 8$ .

$\frac{3}{4} \cdot 5 + b = - 8$

Multiply $\frac{3}{4} \cdot 5$ .

Combine $\frac{3}{4}$ and $5$ .

$\frac{3 \cdot 5}{4} + b = - 8$

Multiply $3$ by $5$ .

$\frac{15}{4} + b = - 8$

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

Subtract $\frac{15}{4}$ from both sides of the equation.

$b = - 8 - \frac{15}{4}$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$b = - 8 \cdot \frac{4}{4} - \frac{15}{4}$

Combine $- 8$ and $\frac{4}{4}$ .

$b = \frac{- 8 \cdot 4}{4} - \frac{15}{4}$

Combine the numerators over the common denominator.

$b = \frac{- 8 \cdot 4 - 15}{4}$

Simplify the numerator.

Multiply $- 8$ by $4$ .

$b = \frac{- 32 - 15}{4}$

Subtract $15$ from $- 32$ .

$b = \frac{- 47}{4}$

Move the negative in front of the fraction.

$b = - \frac{47}{4}$

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.

$y = \frac{3}{4} x - \frac{47}{4}$