Find the Equation with a Point and Slope 4/5 , (-15,5)

$\frac{4}{5}$ , $(- 15, 5)$

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.

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

Substitute the value of $x$ into the equation.

$y = (\frac{4}{5}) \cdot (- 15) + b$

Substitute the value of $y$ into the equation.

$5 = (\frac{4}{5}) \cdot (- 15) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{4}{5} \cdot - 15 + b = 5$ .

$\frac{4}{5} \cdot - 15 + b = 5$

Simplify each term.

Cancel the common factor of $5$ .

Factor $5$ out of $- 15$ .

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

Cancel the common factor.

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

Rewrite the expression.

$4 \cdot - 3 + b = 5$

Multiply $4$ by $- 3$ .

$- 12 + b = 5$

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

Add $12$ to both sides of the equation.

$b = 5 + 12$

Add $5$ and $12$ .

$b = 17$

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.

$y = \frac{4}{5} x + 17$