Graphing Lines using Intercepts - Problem 1
You can graph a line in any form by finding the intercepts. To find the x-intercept, set y equal to 0, then solve for x. The result will be the x-coordinate of the x-intercept (the y-coordinate is 0). To find the y-intercept, set x equal to 0, then solve for y. The result will the be y-coordinate of the y-intercept (the x-coordinate is 0). Graph and connect the two points with a line.
One of the methods you guys might use to graph the equation of a line is by finding both intercepts and connecting them. It doesn’t matter what form the equation is in when you start this process. This equation is in a standard form, but this process would still work even if it was in one of the other forms of equations.
To find the x intercept, I’m going plug in y equals 0. If I substitute in y equals 0 to this equation, I’m just going to cover up this term right here because 4 times 0 is 0. What I’m working with -2 times what number equals 8, I can do that in my head -2 times -4, so my x value is going to be -4. My y value is 0, that’s my x intercept.
The next thing I’m going to do is find the y intercept by putting in x equals 0. Similarly to before, I’m going to cover up the x term because -2 times 0 is 0, so what I still need to think about in my head if 4 times what y value gives 8, y is going to be 2. Be really careful that you write this as two separate points. A lot of times in my class room, I see students who get confused and they write this. They write (-4,2) they think it’s one point. These are actually two different points, so make sure you keep them separate and it’s going to make a lot more sense when you go to graphing.
Just go ahead and graph it. First we’ll get the x intercept on the x axis. The x axis, remember is horizontal and we want the point (-4,0) ther5e it is. The y intercept was (0,2), so I’m going to put my y value right there and then whenever you’re graphing a line, you really want to be careful to use a ruler, that way you’ll now you’re being precise.
So I’m going to set up my ruler so I go exactly through those two points. Draw the line that connects them, and then also make sure you put arrows on the end to show that this line continues forever and ever in both directions. It doesn’t just stop after those two points. It continues on and on and that’s what the arrow show.
So if you’re asked to find how to graph an equation. If you’re asked to find the graph of an equation, you have lots of different choices for how to proceed. If the equation is in standard form, a lot of times people will choose to use intercepts because it’s pretty quick. It’s only a few different steps to find the whole graph of the line.