Question

Use point-slope form to write the equation of a line that passes through the point(8, 18) with slope -7/6

Answer 1

SOLUTION

The equation of a line in point-slope form is given by the formula

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m = slope } \end{gathered}$

From what we are given,

$\begin{gathered} m=-\frac{7}{6} \\ x_1=8 \\ y_1=18 \end{gathered}$

Substituting the values, we have

$\begin{gathered} y-y_1=m(x-x_1) \\ y-18=-\frac{7}{6}(x-8) \\ y-18=-\frac{7}{6}x+\frac{28}{3} \\ y=-\frac{7}{6}x+\frac{28}{3}+18 \\ y=-\frac{7}{6}x+\frac{82}{3} \end{gathered}$

Hence, the answer is

$y=-\frac{7}{6}x+\frac{82}{3}$