Find the Equation with a Point and Slope What is the equation of the line that passes through the point (6,-4) and has a slope of -1/6 ?

What is the equation of the line that passes through the point $(6, - 4)$ and has a slope of $- \frac{1}{6}$ ?

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.

$y = (- \frac{1}{6}) \cdot x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$- 4 = (- \frac{1}{6}) \cdot (6) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{1}{6} \cdot 6 + b = - 4$ .

$- \frac{1}{6} \cdot 6 + b = - 4$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{- 1}{6} \cdot 6 + b = - 4$

Cancel the common factor.

$\frac{- 1}{6} \cdot 6 + b = - 4$

Rewrite the expression.

$- 1 + b = - 4$

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

Add $1$ to both sides of the equation.

$b = - 4 + 1$

Add $- 4$ and $1$ .

$b = - 3$

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.

$y = - \frac{1}{6} x - 3$

Step 3