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Finding the Slope of a Line from 2 Points - Problem 2
Given two points, one which has a missing value, and the slope of a line, you can find the missing value by using the slope formula: m=(y2-y1)/(x2-x1). Plug in the known values and solve for the unknown variable using inverse operations as you would solve any equation.
I’m going to give you guys a little of a secret; this is the Math teacher’s favorite kind of problem. I’m a Math teacher, so I know. Math teachers love this stuff. Find the value if y if the slope of the line that contains 2, 3 and 4, y is 5/2. This is something that you’re probably going to see in your homework, and if it’s not on your homework, you guys it’s probably going to be on your test, that’s like a little secret.
Okay, so in order to do this problem, I wouldn’t be able to solve it by graphing because I wouldn’t know where to put that point, I couldn’t draw both points draw both points and use my counting strategies. I’m going to have to use this formula for slope that you guys have memorized. In order to solve that formula, excuse me to use that formula to find the slope; I’m going to use this as x1 and y1, this I’m going to call x2 and y2 when I’m plugging things in to find out my slope value.
So let’s use the formula y2 take away y1, it’s going to be y minus 3, down at the bottom I have x2 take away x1, so 4 take away 2. This is my slope ratio, and I know it’s supposed to be equal the 5/2, they told me the slope equal 5/2, so I’m going to write that here. 5/2, my slope is equal to what I got out of this formula. From here, this is just a problem that you guys can solve using your solving techniques. What you’d want to do is simplify this side, and then since we have a proportion which is two equal fractions, you might try something like cross multiplying.
I’ll show you what I mean, the 5/2 part is going to stay the same because there is no simplifying there, y take away 3 I can’t simplify, but 4 take away 2 on the bottom there is just going to be 2. Some of you guys might recognize that since these two fractions have the same denominators, I could just work with the tops, and do this in like one easy step. Let’s just say you didn’t know that shortcut, most people when they get to this problem, get to this step will cross multiply and that’s when you say the products of the diagonal quantities are equal to each other, so 5 times 2 is going to be equal to y take away 3 times 2.
So next thing I’m going to do is simplify this doing some distributing and multiplying, distribute, add 6 to both sides so now I’m solving for y getting y all by itself and I can see that 2 times what number gives me 16, oh yeah 8, y has to be 8.
I think this problem is pretty cool like I told you earlier because you have to use a couple of different Algebra techniques. You have to know how to use this formula, you have to be able to set up the proportion correctly, you have to be able to solve that proportion all without making any mistakes. So you guys have all the tools problems like this, I think the hardest point is knowing how to get started. And again the way I knew how to start with this formula is because I couldn’t graph that point. There is no way I could put the dot at four or y if I don’t know what y is.