Aravind S. answered • 04/15/20

Perfect ACT Scorer (36) with Math Knowledge up to Multivariable Calc

What you need to know about perpendicular lines is that they have the **negative reciprocal **slope of the line they are perpendicular to. What this means is that you take the first line's slope, add a negative sign, and switch the numerator and denominator, and that's the slope of the perpendicular line!

In this question, y=2x-1 is our original line. Using the formula y=mx+b, where "m" is the slope, we can see that our "m" in this case is 2. So, negate 2. It becomes -2. Then, switch numerator and denominator. -2 is really -2/1, so let's make it -1/2. That's the slope of the perpendicular line.

Now, we have to make it pass through (-2,6). So right now, all we have is a line like this: y=-1/2x

If we plug in the x-coordinate of our desired point, -2, we get y=-1/2(-2), so y=1. But wait, isn't y supposed to equal 6, since that's the y-coordinate we were given? Yes! So all you need to do is get from 1 to 6, which we can do by adding 5!

So the new equation is y=-1/2x+5!