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jenyasd209 [6]
3 years ago
7

Consider the line

="absmiddle" class="latex-formula">
Find the equation of the line that is perpendicular to this line and passes through the point (5 , 2)

Find the equation of the line that is parallel to this line and passes through the point ( 5 , 2)

Equation of perpendicular line:

Equation of parallel line:
Mathematics
1 answer:
Oksanka [162]3 years ago
8 0

Firstly we put the equation of the line into y=mx+c form so we can find the gradient.

-5x-4y=7 \Rightarrow -5x-7=4y \Rightarrow \frac{-5}{4}x-\frac{7}{4}=y

So we see the gradient of the line is -5/4. The gradient of a line perpendicular to a line with gradient m is -\frac{1}{m} so we see the gradient of a line perpendicular to your line is -\frac{1}{-\frac{5}{4}} = \frac{4}{5}.

So we know it's a line with gradient 4/5 passing through (5,2) hence

y-2=\frac{4}{5}(x-5) \Rightarrow y-2=\frac{4}{5}x-4 \Rightarrow y=\frac{4}{5}x-2.

For the parallel line, you use the same gradient as the original which is -5/4 and using the fact that it passes through (5,2) repeat the process from above to find the line. I'll leave this one up to you!

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