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Point-Slope Form of Linear Equations - Problem 1

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

To find the equation of a line when given a point on a line and the slope, use point-slope form: y-y1=m(x-x1). The values of x1 and y1 are the coordinates of the given point. Plug the values for m (the slope), x1 and y1 into the point-slope form. Then solve for y in order to write the equation in slope-intercept (y=mx+b) form.

A lot of times you see problems with directions like this that are a little bit vague. Here is what I mean.

It says write the equation for the line that has slope -2/3 and contains the point (6,-1). That might sound clear to you, but because I’m a big Math nerd, I know that there’s lots of different ways to write the equation. They didn’t specify if they wanted Point-Slope form, or Slope-Intercept form or even Standard Form. So I’m just going to go ahead and show you a couple of different forms that you can get from this problem pretty easily.

The first thing I know is I’m given a slope and a point, so in my head I’m thinking slope and a point, so I’m going to use Point-Slope form which looks like this. This is something you’re going to want to memorize if you don’t have it memorized already.

When I fill in numbers that x and that y are going to stay with the letters x and y, everything else is going to get replaced by what’s given to me in the problem. Like for example m stands for my slope number, so instead of m I’m going to write -2/3, then this is going to be my x sub 1 value, that’s going to be my y sub 1 value and I’m going to plug it in. y minus -1 equals -2/3, that was my slope number times x minus x sub 1. If I distribute this negative sign, and take care of this minus, minus I’ll have y plus 1 equals -2/3x minus 6.

Now since this problem’s directions were kind of vague, I might be done right here. This is the Point-Slope form of this equation, and the reason I know it’s that form is because it’s the way simplified, I took care of those negative signs.

However, let’s just say that this problem had asked for the Slope-Intercept form, that’s y equals mx plus b. I would have to do just a little more Math and I’ll show you what I mean. In order to get from this form to slope intercept form, I’m going to have to distribute, and then get y all by itself. It’s a quick process. Let me how you how it goes.

Here is my problem or my equation. First thing I’m going to be doing is distributing that -2/3 to simply. -2/3x, and then -2/3 times -6 is going to become +12/3 which reduces to 4. I’m almost done. In order to have it in this form I need to have y all by itself, so I still need to subtract one from both sides, and I’ll have y equals -2/3x plus 3, this is the Slope-Intercept form.

So again, this is the exact same line, just written in different formats, and if you’re textbook was vague like this, just stop there. If it didn’t tell you what form it wants boom say hey teacher I got the Point-Slope form, I’m done. Just be careful, a lot of times, books or teachers will ask you to use the Point-Slope form in order to get to the Slope-Intercept form. Just make sure you’re reading directions carefully, and you guys will get these problems correct.

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