Chapter 2 - Graphs and Functions - 2.5 Equations of Lines and Linear Models - 2.5 Exercises - Page 244: 60

(a) $2$ (b) $-6$

(a) As the line is parallel to $2x-3y=4$, the slope is $m=\frac{2}{3}$, thus we have $\frac{r-6}{-4-2}=\frac{2}{3}$ which gives $r=2$ (b) As the line is perpendicular to $x+2y=1$ (which has a slope of $-\frac{1}{2}$), the slope of the required line is $m=2$, thus we have $\frac{r-6}{-4-2}=2$ which gives $r=-6$