To write the equation of a line given the slope and a point on the line, you can use the slope-intercept form of the line and plug in the given values. Plug in the value of the slope for m, and the coordinates of the given point into the x and y variable. Next, solve for the unknown, b (the y-intercept). Once you determine the value of the y-intercept, write the equation of the line with the value of the slope, the value of the y-intercept, and the variables x and y.
This is a situation where I’m asked to find the slope intercept form of the equation of a line and I’m given the slope, so that’s good, but I’m not given the y-intercept, that’s kind of tricky. I’m given another point on the line.
There is a couple different ways to solve this. Some of you guys you already know what’s called the point-slope equation and it looks like this. If this makes sense to you, go ahead and use this method. If that doesn’t make any sense for you, hang on we’re going to get to another method in just a second.
Another way you could do this problem would be to graph it, would be to draw the point (-4,-5). I’m just doing this really rough sketch and then count the slope until I find the y-intercept. My slope is +2, so I go up two over one, up two over one and keep doing this until I find the y-intercept. This would be useful if you had a graph paper, but if you’re like me and you don’t have graph, that might not be the best method either.
One way you can do it is by using my favourite equation, the slope-intercept form and plugging stuff in. Like for example we have an x value and a y-value and we know the slope, the thing I don’t know is the b, or the y-intercept. I’m going to plug all this stuff in and find b, check it out. My y value is -5, my slope number is 2, my x number is -4, and then I’m trying to find out what b is there. By the way, I mean for that to be the letter b and not the number 6. Sometimes it’s hard to tell because people’s handwriting makes it look like a 6, that’s a b.
Okay, so now I have -5 equals –a plus b, add 8 to both sides and I’ll get my y-intercept equals 3. Now this problem I’m almost there. It’s going to be like 10 more seconds because I want my equations to look like that, I’ll start with y equals slope number is 2, my y-intercept number is 3. That’s it, I had to do a little bit of an extra step because they didn’t tell me the y-intercept, I had to find it using this method, but use the information that’s given. You’re given the slope, and you’re given an x value and a y value, so substitute it then and find your b that way. This is one way to do this problem.
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