Writing equations given the points

Question

Write the equation of the line perpendicular to the line 5x+2y=24 and passing through (8,-12).

Can you walk me through how to do this and give me another example?

Answer 1

First, find the slope of your line by solving for y:

y = 12 - (5/2)x. The slope is -5/2.

The line perpendicular has slope 2/5. This is because the product of the slopes of a line and its perpendicular line is -1.

Therefore, the perpendicular line has an equation of the form:

y = (2/5)x+b. We use the desired point on this line to find b.

-12 = y(8) = (16/5)+b. So, b = -12-16/5 = -76/5.

So, the equation of the perpendicular line is

y = (2/5)x - 76/5.

Answer 2

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