## Intermediate Algebra (12th Edition)

We know that two parallel lines have the same slope ($m_1=m_2$). We also know that perpendicular lines have negative reciprocal slopes ($m_1=-\frac{1}{m_2}$). To calculate the slope between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the formula: $slope=m=\frac{y_2-y_1}{x_2-x_1}$ We calculate the slope between the points $(4,\ 6)$ and $(-8,7)$: $slope=m=\displaystyle \frac{7-6}{-8-4}=\frac{1}{-12}=-\frac{1}{12}$ Next, we calculate the slope between the points $(-5,5)$ and $(7,\ 4)$: $slope=m=\displaystyle \frac{4-5}{7-(-5)}=\frac{-1}{12}=-\frac{1}{12}$ We see that the slopes are equal. Thus the lines are parallel.