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Point-Slope Form of Linear Equations - Problem 2

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 write the equation of a line given two points on the line, start by finding the slope. Remember that slope is the change in the y-values over the change in the x-values, or (y2-y1)/(x2-x1). Use the given points. One point is (x1, y1) and the other point is (x2, y2). It does not matter which is (x1, y1) and which is (x2, y2). Plug in the values and simply. The result is the value of the slope. Then use point-slope form y-y1=m(x-x1), and plug in the slope you just calculated and one of the given points. Plug in the values for m, x1 and y1. Simplify, then solve for y in order to put the equation into slope-intercept (y=mx+b) form.

This is a problem where all I’m given is two points and I’m asked to find the equation and put it into Slope-Intercept form. This problem is going to show up in you homework or on your test for sure. This type of problem is all over in Math.

So let’s go ahead and start this. The first thing I know is that this is a line, so it’s going to have a constant slope, and in order to find the slope, I’m going to use this formula y2 minus y1 over x2 minus x1. Once I know the slope, I’ll be able to use either point I can pick which one into the Point-Slope form which looks like this, that’s the Point-Slope form of an equation because it uses a point and a slope. I’ll use the slope in here with one of my points and then I’m still going to have to simplify it to get it into Slope-Intercept form which looks like y equals mx plus b.

Notice I haven’t done any Math yet; all I’ve done is like collect the formulas I’m going to need to use in order to do this problem. That’s why to do this problem, you’re going to need to know lots of Math and therefore teachers like to put it on tests. They like to put it in their homework to see what, you know.

Okay so here we go. The first thing I’m going to do is find the slope. I’m going to label this x1, y1 label that x2, y2 and then to find the slope, I’ll do y2 take away y1 on top of x2 take away x1. Be really careful with your negative signs. When I simplify that I’ll have -6 over -12 which reduces to +1/2. That’s my slope number.

Now when I put it into Point-Slope form, I could use either point. I can choose whatever one I want to. I personally I’m not a huge fan of negatives. I can do them, but it gives me more opportunities to make mistakes, so I’m going to choose that point. That point has too many negatives. Either way I should get then same answer.

Okay so let’s see. In Point-Slope form I’ll have y minus 3 equals my slope number times x take away my x value. That’s Point-Slope form of the equation. I’m almost there. I have an equation, but they want me to turn it into slope intercept. Remember slope intercepts look like this, I need to get y all by itself.

In order to do that I’m going to have to some simplifying on the right side first by distributing that one half, half of -4 is -2. Then I’m almost done. Last thing I need to do is get y isolated by adding 3 to both sides, so I’ll have y equals 1/2x plus 1. That’s my final answer. This is the Slope-Intercept form. That was the Point-Slope form. That was the slope oh my gosh there’s turns of vocabulary in this problem and you guys again that’s why this problem is classic in your Math classes. I promise you it’s going to show up, so you might want to watch this video a couple of times until you feel absolutely solid with all of these different processes.

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