Standard Form of Linear Equations - Problem 3
If the equation of a line is in standard form, the easiest method to graph the line is by finding intercepts. Remember that at the y-intercept, the x coordinate is equal to 0, and that at the x-intercept, the y coordinate is equal to 0. To find the y-intercept, set x equal to 0 and solve for y. Likewise, to find the x-intercept, set y equal to 0 and solve for x. Plot the two intercepts, and graph the line.
Any time you're asked to graph a linear equation, you have a choice of options for how you want to approach it. You might choose to make a table of values. You might choose to put it into y equals mx plus from and use slope intercept, or you might choose to find the x, and y intercepts and connect them.
Standard form for many people, they find it easiest to use the intercepts method. They also use what some people call it covering up. Here is what I mean. We know that in order to find the x intercept, we want to let y equal to 0.
So in this problem, if I have y equal to 0, I'm just going to cover that up, because 3 times 0 becomes 0. What I'm really working with then is 2x equals -6. 2 times what number is -6? -3. So I would have x equals -3. That's my x intercept. That's going to be one of the points I'll put on my graph.
The other point I'm going to do is the y intercept by using x equals 0. Here I'm going to cover up my x term, because 2 times 0 is 0, and I'm left with 3 times what number gives me -6. That answer is -2. So my y intercept is going to look like 0 for x, -2 for y.
So now that I'm asked to graph it, I'm just going to plot those two points, and connect them. This is going to be a rough graph, because I don't have any graph paper handy, but you'll see how it works anyway.
My first point goes at -3, 0 that's my x intercept. My second point goes at 0, -2. The last thing I'm going to do is connect them. If you guys had a ruler, you would do that perfectly. It would be even more exquisite if you had graph paper.
I just wanted to give you guys a general idea of how you can use intercepts to graph a line, especially quickly when it's already in standard form.