By: Brooke Norman
Day 3:
Graphing a Linear Equation Using The X- and Y- Intercepts.
Objectives:
1- To understand what an x- and y- intercept is.
2- To learn how to find the x- and y- intercepts of a given equation.
3- To learn how to graph a given equation using the x- and y- intercepts.
1- Using the x- and y- intercepts to graph an equation can be a very useful technique. A student must fully understand what the x- and y- intercepts are and how to find them. It would be helpful if the teacher had an overhead of a piece of graph paper. There are even apparatuses that can hook up to a graphing calculator and project it on an overhead that can be useful if they are available. Once the graph is displayed, explain to the students what an intercept is. Ask them if they have any clues or ideas as to what an intercept is. The first thing that comes into most students minds will be something along the lines of an interception in football. Explain this to them and then relate it x- and y- intercepts. Tell them to look for where the line of the graph crosses the x-axis and y-axis. Make clear that the x-intercept is where the graph crosses the x-axis and the y-intercept is where the graph crosses the y-axis.
2- So how do you find the x- and y- intercepts? Have the students figure out the coordinates of the points where the line crosses the x- and y- axis. The students should find that where the line crosses the y- axis, the ordered pair is (0, y). They will also find that where the line crosses the x-axis, the ordered pair is (x, 0). It may take a few examples in order for the students to figure it out, realizing this is true for every graph. This would be a good time to use the graphing software to show the students that this happens with all x- and y- intercepts. When the students are sure of this new concept, give them some examples to have them work on their own. Remind them of the steps they need to take in order to draw the graph. Now ask them how to find the coordinate of the y-intercept. By now, they should be able to tell you that it is where x is equal to 0. At this time, ask them if they can find the x-intercept. This may be a little more difficult for the students. They are use to solving an equation by substituting an x value into an equation solved for y. This is the opposite of that. They will now have to set the equation equal to 0 and solve for x or they can solve the equation for x and set the y equal to 0. It takes a little more work than they are previously used to. Go over some examples like:
3x + 5y = 45
X-intercept: solve for y
y= (45-3x)/5
Substitute in 0 for x
y= (45-3(0))/5
y=45/5
y=9
Or
Substitute in 0 for x from the beginning
3(0) + 5y= 45
5y=45
y=9
X-intercept is (0, 9)
--------------------------------------------
3x + 5y = 45
Y-intercept: solve for x
3x=45-5y
x= (45-5y)/3
Substitute in 0 for y
x= (45-5(0))/3
x=45/3
x=15
Or
Substitute 0 in for y from the beginning
3x+5(0) =45
3x=45
x=15
The coordinate for the y-intercept is
(15, 0)
3- Now that the students have a table of points, the x-intercept coordinate, and the y-intercept coordinate, have the start plotting the points of this equation on their graph paper. Teach them to label the points as they are plotted, it allows them to visualize what is going on. It also helps with students that are visual learners to grasp the concepts and ideas a little easier. The teacher should be doing this on the overhead at the same time as the students. Give them several tries with different equations to get some practice on this matter and to make sure they fully understand what they are doing. This can be turned into a group work situation or some kind of game. Varying the type of instruction is helpful in keeping the studentsÕ interest.
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