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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?

1 Answer

Konstantinos Michailidis

Sep 11, 2015

Refer to explanation

Explanation:

We write line m as follows

$8 x - 7 y + 10 = 0 \Rightarrow 7 y = 8 x + 10 \Rightarrow y = \frac{8}{7} x + \frac{10}{7}$ $8x-7y+10=0=>7y=8x+10=>y=8/7x+10/7$

and $k x - 7 y + 10 = 0 \Rightarrow y = \frac{k}{7} x + \frac{10}{7}$ $kx-7y+10=0=>y=k/7x+10/7$

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

in order to be perpendicular we have that

$\frac{8}{7} \cdot \frac{k}{7} = - 1 \Rightarrow k = - \frac{49}{8}$ $8/7*k/7=-1=>k=-49/8$

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