Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-5,3) and has a slope of -6/5 ?

What is the equation of the line that passes through the point $(- 5, 3)$ and has a slope of $- \frac{6}{5}$ ?

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.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Simplify each term.

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

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

Factor $5$ out of $- 5$ .

$\frac{- 6}{5} \cdot (5 (- 1)) + b = 3$

Cancel the common factor.

$\frac{- 6}{5} \cdot (5 \cdot - 1) + b = 3$

Rewrite the expression.

$- 6 \cdot - 1 + b = 3$

Multiply $- 6$ by $- 1$ .

$6 + b = 3$

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

Subtract $6$ from both sides of the equation.

$b = 3 - 6$

Subtract $6$ from $3$ .

$b = - 3$

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.

$y = - \frac{6}{5} x - 3$

Step 3