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

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

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3}{5}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$- 3 + b = - 6$

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

Add $3$ to both sides of the equation.

$b = - 6 + 3$

Add $- 6$ and $3$ .

$b = - 3$

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.

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

Step 3