# Write an equation of a line perpendicular to a given line and contains points

So the slope here is equal to 2.

This is already in slope-intercept form. Are these lines parallel? The perpendicular slope being the value of "a" for which they've asked me will be the negative reciprocal of the reference slope. What is the slope of B?

So this right here is a negative 4. The distance will be the length of the segment along this line that crosses each of the original lines. If your preference differs, then use whatever method you like best. Therefore, there is indeed some distance between these two lines.

But I don't have two points.

## How to find perpendicular line

It's up to me to notice the connection. Ah; but I can pick any point on one of the lines, and then find the perpendicular line through that point. So what we'll do is figure out the slope of A, then take the negative inverse of it. Clicking on "Tap to view steps" on the widget's answer screen will take you to the Mathway site for a paid upgrade. And we are done. Then my perpendicular slope will be. Yes, they can be long and messy. If your preference differs, then use whatever method you like best. That intersection point will be the second point that I'll need for the Distance Formula. Content Continues Below You can use the Mathway widget below to practice finding a perpendicular line through a given point. The slope of A is right there, it's the 2, mx plus b. You can use the Mathway widget below to practice finding a parallel line through a given point. I'll leave the rest of the exercise for you, if you're interested. And they say that the line B contains the point 6, negative 7. With this point and my perpendicular slope, I can find the equation of the perpendicular line that'll give me the distance between the two original lines: Okay; now I have the equation of the perpendicular.

I'll leave the rest of the exercise for you, if you're interested.

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