Chapter 10 - Section 10.2 - Graphs of Linear Equations and Slope - Exercises - Page 465: 25

23

Let $m_1$ and $m_2$ denote the slopes of the two lines. $m_1=\frac{2-(-3)}{3-2}=\frac{5}{1}=5$ $m_2=\frac{-1-4}{x-(-2)}=\frac{-5}{x+2}$ By Theorem 10.2.2, we want $m_1*m_2=-1$. So $5*\frac{-5}{x+2}=-1$. $\frac{-25}{x+2}=-1$ $-25=-x-2$ $-23=-x$ So $x=23$.