A line passes through (2,4) and (7,3). A second line passes through (8,5). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Burglar
Jun 1, 2016

It is y=−15x+335.

Explanation:

We start calculating the slope of the line passing by the first two points.

The generic question is
y=mx+q
substituting the points we have
4=2m+q
3=7m+q
From the first equation I have
q=4−2m
I substitute this value in the second equation
3=7m+4−2m then
−1=5m and
m=−15.

Now we know that all the lines with the same slope are parallels.
So the line passing by the third point has equation

y=−15m+q and we have to find the q imposing the passage from (8,5).

5=−15⋅8+q

q=5+85=335

Then the equation of the desired line is

y=−15x+335.

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