Find the Equation Using Slope-Intercept Form (-7,9) ; m=4/5

$(- 7, 9)$ ; $m = \frac{4}{5}$

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.

$y = (\frac{4}{5}) \cdot (- 7) + b$

Substitute the value of $y$ into the equation.

$9 = (\frac{4}{5}) \cdot (- 7) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{4}{5} \cdot - 7 + b = 9$ .

$\frac{4}{5} \cdot - 7 + b = 9$

Simplify each term.

Multiply $\frac{4}{5} \cdot - 7$ .

Combine $\frac{4}{5}$ and $- 7$ .

$\frac{4 \cdot - 7}{5} + b = 9$

Multiply $4$ by $- 7$ .

$\frac{- 28}{5} + b = 9$

Move the negative in front of the fraction.

$- \frac{28}{5} + b = 9$

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

Add $\frac{28}{5}$ to both sides of the equation.

$b = 9 + \frac{28}{5}$

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = 9 \cdot \frac{5}{5} + \frac{28}{5}$

Combine $9$ and $\frac{5}{5}$ .

$b = \frac{9 \cdot 5}{5} + \frac{28}{5}$

Combine the numerators over the common denominator.

$b = \frac{9 \cdot 5 + 28}{5}$

Simplify the numerator.

Multiply $9$ by $5$ .

$b = \frac{45 + 28}{5}$

Add $45$ and $28$ .

$b = \frac{73}{5}$

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.

$y = \frac{4}{5} x + \frac{73}{5}$