# The equation of line m is 8x-7y+10=0. a. For what value of k is the graph kx-7y+10=0 parallel to line m? b. What is k if the graphs of m and kx-7y+10=0 are perpendicular?

Refer to explanation

#### Explanation:

We write line m as follows

$8 x - 7 y + 10 = 0 \implies 7 y = 8 x + 10 \implies y = \frac{8}{7} x + \frac{10}{7}$

and $k x - 7 y + 10 = 0 \implies y = \frac{k}{7} x + \frac{10}{7}$

So to be parallel k must be $k = 8$

in order to be perpendicular we have that

$\frac{8}{7} \cdot \frac{k}{7} = - 1 \implies k = - \frac{49}{8}$