Find the Equation with a Point and Slope m=9/5 , (8,-4)

$m = \frac{9}{5}$ , $(8, - 4)$

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.

$y = (\frac{9}{5}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{9}{5}) \cdot (8) + b$

Substitute the value of $y$ into the equation.

$- 4 = (\frac{9}{5}) \cdot (8) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{9}{5} \cdot 8 + b = - 4$ .

$\frac{9}{5} \cdot 8 + b = - 4$

Multiply $\frac{9}{5} \cdot 8$ .

Combine $\frac{9}{5}$ and $8$ .

$\frac{9 \cdot 8}{5} + b = - 4$

Multiply $9$ by $8$ .

$\frac{72}{5} + b = - 4$

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

Subtract $\frac{72}{5}$ from both sides of the equation.

$b = - 4 - \frac{72}{5}$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = - 4 \cdot \frac{5}{5} - \frac{72}{5}$

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

$b = \frac{- 4 \cdot 5}{5} - \frac{72}{5}$

Combine the numerators over the common denominator.

$b = \frac{- 4 \cdot 5 - 72}{5}$

Simplify the numerator.

Multiply $- 4$ by $5$ .

$b = \frac{- 20 - 72}{5}$

Subtract $72$ from $- 20$ .

$b = \frac{- 92}{5}$

Move the negative in front of the fraction.

$b = - \frac{92}{5}$

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.

$y = \frac{9}{5} x - \frac{92}{5}$

Step 3