Question

152 chapter 3 functions and graphs
exer. 17 - 18: write equations of the lines.
17
(2, - 3)

Explanation:

Step1: Find slope of first line

The first line passes through $(2,-3)$ and has a rise - run relationship shown. For a right - triangle with rise 5 and run 4, the slope $m_1=\frac{5}{4}$. Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(2,-3)$, we have $y+3=\frac{5}{4}(x - 2)$. Expanding gives $y=\frac{5}{4}x-\frac{5}{2}-3=\frac{5}{4}x-\frac{5 + 6}{2}=\frac{5}{4}x-\frac{11}{2}$.

Step2: Find slope of second line

The second line is perpendicular to the first one. If two lines with slopes $m_1$ and $m_2$ are perpendicular, $m_1m_2=-1$. Since $m_1 = \frac{5}{4}$, then $m_2=-\frac{4}{5}$. Using the point - slope form with $(x_1,y_1)=(2,-3)$, we get $y + 3=-\frac{4}{5}(x - 2)$. Expanding gives $y=-\frac{4}{5}x+\frac{8}{5}-3=-\frac{4}{5}x+\frac{8 - 15}{5}=-\frac{4}{5}x-\frac{7}{5}$.

Answer:

The equations of the lines are $y=\frac{5}{4}x-\frac{11}{2}$ and $y=-\frac{4}{5}x-\frac{7}{5}$