Graphing y = mx + bDate: 01/20/97 at 10:58:13 From: Larry Shirley Subject: x and y intercepts and graph Dear Dr. Math, I am having trouble understanding 3x + 2y = 5. This has to be in y = mx + b form. After I get it in the proper form, how do I graph it? Sarah Date: 01/20/97 at 11:59:07 From: Doctor Lisa Subject: Re: x and y intercepts and graph Hi Sarah! Let's take a look at your question step by step. The first thing you told me is that you need to get the equation into y = mx + b form. So, to begin, you will work on solving this equation for y. As you may recall, what that means is that you want to manipulate the equation so you get y by itself on one side of the equation. This is the process I would use: 3x + 2y = 5 2y = -3x + 5 (subtract 3x from each side to get 2y by itself) y = -3/2x + 5/2 (divide both sides by 2 to get y by itself) Now that I have the equation in the proper form, we're ready to graph it. Remember that y = mx + b is called "slope-intercept form." If you have an equation in this form (and written with the x-term first and the constant second), you will have the slope and the y-intercept for the graph. The slope is "m" (the coefficient of x) and is the rise over the run (or the change in y over the change in x). The y-intercept is "b" and is where the graph crosses the y-axis. In this problem, m = -3/2 and b = 5/2. I would first locate the y-intercept on the graph. Since b = 5/2, I would find where 5/2 (or 2 1/2) is on the y-axis and make a point. This is where the graph crosses the y-axis. From there, I would use the slope to find other points on the graph. When using slope, we first travel in the y direction and then move in the x direction. Keep in mind that a positive y direction is up, a negative y direction is down, a positive x direction is right, and a negative x direction is left. When you have a positive slope, you will either use a positive y and positive x movement or a negative y and negative x direction. This is because a positive number divided by a positive number is still positive and a negative number divided by a negative number is also positive. Since we have a negative slope, we need one positive number and one negative number. ** As I am describing the graphing process below, I am assuming that you are using graph paper. This process will work with any scale on the graph (1 square could equal 2 units or 10 units, etc.). ** Our slope is -3/2. This means I can do one of two things: either go up 3 squares (positive direction) and left 2 squares (negative direction) or go down 3 squares (negative direction) and right 2 squares (positive direction). Be careful with this problem because you are beginning with a fraction (the 5/2 from above) - you'll have to either estimate where halfway is or make each mark equal to 1/2 (in other words, 2 marks on the graph = 1 unit). Go to the 5/2 you marked earlier. You can go up 3 squares from the 5/2 and then move over left 2 squares and make your next point. You can also go down 3 squares from the 5/2 and then move over right 2 squares and make your next point. If you do both of those operations, you will have 3 points and can connect the dots to make a line. You can count out as many points as you need to make the line, but I suggest a minimum of 3 points for accuracy (although some teachers want you to use 5 points). The more points you have, the more accurate the line will appear on your graph. I hope I clearly answered your question for you and that this will help you do other problems similar to it. Have a great day! -Doctor Lisa, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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