Question

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

Answer 1

`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