1) To understand what is an x and y intercept
2) To learn how to find the x and y intercept of a given equation
3) To learn how to graph a given equation using the x and y intercept
1) Using the x and y intercept to graph an equation is a powerful tool, but a student must first understand what the x and y intercept are and where they can be found. I would start with a graph on an overhead or, better yet, a graph from a graphing calculator or some graphing software. With the graph up so everyone can see, discuss first what is meant by intercept. From a sports point of view, I would think about football. When a pass is intercepted, that means that the ball, that was on a line from the quarterback to the receiver, was caught by the defensive player as their paths crossed. So, is there any thing that this line crosses? Well, yes, the x and y axis. Okay, then if we want to find the x and y intercept, then where would we look? Well, the x intercept is where the line crosses the x axis and the y intercept is where the line crosses the y axis.
2) Now, if given a particular equation, how could we find the x and y intercept? Using the same graph from above, ask your students what the ordered pair is where the line crosses both the x and y axes. They will find that where the line crosses the x axis, the ordered pair is (x,0), in general. And for the y intercept, (0,y). One graph will not be enough. Now, using the graphing calculator or the graphing software, show them several other graphs and let them see for themselves that the general case is what was stated above. When they are convinced of this, give them an equation, say 2x + 6y = 18. Remind them of the activities of the day before where they had to verify whether ordered pairs were solutions to given equations and when they had to make tables of values. Ask them how could they find the ordered pair for the y intercept. They, surprisingly, will be able to tell you that x has to be 0. Then allow them to find y. This is the same thing they did yesterday. The ordered pair for the y-intercept will be (0,3). Now ask them to find the x intercept. This will not be as obvious because they are used to choosing an x and finding y and are not used to choosing and substituting in for y and then finding x. However, they will see the connection and be able to do this. The ordered pair for the x intercept is (9,0).
3) When they have this, the graph of the equation will be the easy part. On some graph paper, have the students first plot the points that correspond to the ordered pairs, and have them label both points. I am a huge fan of labeling on graphs because I believe that the visual learners will benefit from this. In the mean time, the teacher should be doing the same thing on an overhead piece of graph paper, a pull down wipe-off coordinate plane, or on some software like GSP. Now have them connect the two points and therefore make the graph of the equation. They will need several chances to do this. Provide them with some examples and let them work in pairs or groups. This could be turned into a fun game. For example, give the students the following 5 equations. Have them find the intercepts, plot the point that corresponds to the ordered pair, label the intercepts, and then graph and label the line. That means that for each equation, there are 8 required things to do: find x intercept, find y intercept, plot x intercept, plot y intercept, label x intercept, label y intercept, draw graph, and label graph. Give them a reasonable time limit and let them begin. The team or teams with the most total points gets some kind of award, not reward. Make them the day's math whiz' or something like that. Here are some equations to use:
2x + 4y = 8
3x + 6y = 24
x - 4y = 16
y = 3x + 6
15 = 2x - 3y
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