What is the equation of the line that passes through (-6, 1) and is perpendicular to y = 3/8 x +4?

1 Answer
Akazukin 赤ずきん
Nov 6, 2017

y = -8/3x - 15

Explanation:

Perpendicular lines have slopes that are the negative reciprocal of each other, and since the slope of y = 3/8x + 4 is 3/8, then the negative reciprocal-- aka flipping the number-- would result in -8/3.

Now that we have the slope, we must find the y-intercept so that the point (-6, 1) fits on the line.

To do this, we can simply plug in the x value into our current slope:

x coordinate = -6; slope = -8/3

-8/3 · -6 = 16

y = mx + b

y = 16 + b

If the y coordinate = 1, then subtracting 15 from our current answer will fit the criteria of the graph; in other words, our b value has to be -15.

16 - 15 = 1

Therefore, putting the pieces together will give you y = -8/3x - 15 .

You may plug in the coordinates (-6, 1) back into the equation to check.

Hope this helps!

Best wishes,
A high school student

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