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Graphing Lines using Intercepts - Problem 2 3,433 views

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

When given an equation of a line in slope-intercept form (y=mx+b), you can easily find the y-intercept since the "b" value represents where the line will cross the y-axis. To find the x-intercept, set y equal to 0 and solve for x. The result will be the x-coordinate of the x-intercept (the y-coordinate of the x-intercept is 0).

I’m asked to graph this equation using intercepts. This equation is in y equals mx plus b form which tells me that I already know the y intercept because in y equals mx plus b form, the b represents the y intercept. I know I’m going to have the y intercept of 0 for x, -4 for y. I’ve already done like half of the problem. I already found the y intercept. However, finding the x intercept is a little bit trickier when you’re working with this form of an equation.

Remember that to find an x intercept you want to substitute in y equals 0, so I’m going to have substitute in y equals 0, so I’m going to have 0 equals 3x take away 4 and now I need to solve for x. Add 4 to both sides divide by 3, so I’ll have x equals 4/3. My x intercept is going to be (4/3,0). Those are my two intercepts, the two separate points that I’m going to use to graph this line on my graph.

First let’s get the y intercept on there. 0, 4 means zero side to side, and then down 4 on the y axis. And then this point (4/3,0) is a little tricky because it’s a fraction. I’m just going to be approximating 4/3 is a little bit more than 1, technically it’s 11/3, but whatever, I have these little boxes I’m going to just do my best to go 11/3 in the positive direction, something like that.

Whenever you’re graphing a line, it’s a great idea to have a ruler handy so you can be precise. Make sure your ruler goes through the points as best as you can draw the line that connects them, and then lastly, make sure to put arrows on your points, excuse me on the ends of your line to show that the line continues forever and ever with that same slope.

So guys if you’re given an equation in y equals mx plus b form and you’re asked to graph it using intercepts, the first thing to do is to remember the y intercept jumps out of you is part of the y=mx+b equation, but to find the x intercept, you have to a little bit more Math. Once you have both of those points, stick them on there, connect them and you’re on your way.

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