Find the Equation Using Slope-Intercept Form (-3,-7) ; m=-6/5

$(- 3, - 7)$ ; $m = - \frac{6}{5}$

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.

$y = (- \frac{6}{5}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{6}{5}) \cdot (- 3) + b$

Substitute the value of $y$ into the equation.

$- 7 = (- \frac{6}{5}) \cdot (- 3) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{6}{5} \cdot - 3 + b = - 7$ .

$- \frac{6}{5} \cdot - 3 + b = - 7$

Multiply $- \frac{6}{5} \cdot - 3$ .

Multiply $- 3$ by $- 1$ .

$3 (\frac{6}{5}) + b = - 7$

Combine $3$ and $\frac{6}{5}$ .

$\frac{3 \cdot 6}{5} + b = - 7$

Multiply $3$ by $6$ .

$\frac{18}{5} + b = - 7$

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

Subtract $\frac{18}{5}$ from both sides of the equation.

$b = - 7 - \frac{18}{5}$

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = - 7 \cdot \frac{5}{5} - \frac{18}{5}$

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

$b = \frac{- 7 \cdot 5}{5} - \frac{18}{5}$

Combine the numerators over the common denominator.

$b = \frac{- 7 \cdot 5 - 18}{5}$

Simplify the numerator.

Multiply $- 7$ by $5$ .

$b = \frac{- 35 - 18}{5}$

Subtract $18$ from $- 35$ .

$b = \frac{- 53}{5}$

Move the negative in front of the fraction.

$b = - \frac{53}{5}$

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.

$y = - \frac{6}{5} x - \frac{53}{5}$

Step 3