Find the Equation Using Slope-Intercept Form (7,0) , m=-1/6

$(7, 0)$ , $m = - \frac{1}{6}$

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.

$y = (- \frac{1}{6}) \cdot (7) + b$

Substitute the value of $y$ into the equation.

$0 = (- \frac{1}{6}) \cdot (7) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{1}{6} \cdot 7 + b = 0$ .

$- \frac{1}{6} \cdot 7 + b = 0$

Simplify each term.

Multiply $- \frac{1}{6} \cdot 7$ .

Multiply $7$ by $- 1$ .

$- 7 (\frac{1}{6}) + b = 0$

Combine $- 7$ and $\frac{1}{6}$ .

$\frac{- 7}{6} + b = 0$

Move the negative in front of the fraction.

$- \frac{7}{6} + b = 0$

Add $\frac{7}{6}$ to both sides of the equation.

$b = \frac{7}{6}$

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.

$y = - \frac{1}{6} x + \frac{7}{6}$

Step 3