1. Students will acquire the concept of slope-intercept and point-slope forms of an equation.
2. Students will use a given ordered pair and slope to plot a graph.
3. Students will quickly graph equations given in either form.
4. Students will transform 2-variable linear equations into slope-intercept form.
Graph paper/coordinate plane personal whiteboards
Colored pencils/dry erase markers
Begin by placing the following equation on the board and having students graph it with their partners:
y = -1/2x + 4
After they have graphed the line, ask them to identify the slope of the line and its y-intercept. Lead a discussion where you draw out the observation that the slope and the y-intercept are readily identifiable in the equation itself.
Next, have them graph the following equation, find its slope and its y-intercept:
y = 2x -3
Lead a similar discussion, making sure to highlight the fact that when there is a subtraction sign in the equation, the y-intercept is negative
Next, ask the students to try to graph a line given only its y-intercept and slope. Place the following information on the board:
m = -3/4 y-intercept = (0, -2)
Lead a quick discussion as to how to draw a line from one point and the slope. (Draw out that because of the geometric definition of slope, you can go "up" and "over" from the starting point to find a second point, which will then allow you to draw the line.) Have students draw this line, and challenge them to determine the equation for it (using the above format). Once they have done so, formally introduce slope-intercept form
, defining it and giving some more examples.
Now, put the following equation on the board and ask them to attempt to graph it:
y - 3 = -1/2 (x + 2)
This will undoubtedly take them some time; circulate and help those groups that are struggling. After about 5 minutes, lead a discussion about how those groups that were successful were able to graph it. Point out that it is possible to "manipulate" this equation into the form the other equations were in:
y - 3 = -1/2x -1
y = -1/2x + 2
Point out that any 2-variable equation can be transformed into slope-intercept form using simple Algebra. Leave the above equation on the board and have them transformt the following equation as well:
y + 2 = 2 (x - 4)
Once they have completed this, have them graph both equations (this and the above equation). Highlight the fact that in both equations, the slope and one point on the line are readily visible in the form of the equation (for the first equation, m = -1/2 and the point (-2, 3); for the second equation, m= 2 and the point (4, -2)). Point out that this is another form of an equation that gives information, point-slope form
. Define point-slope form, and then provide the following example to show how it is sometimes more useful than slope-intercept form (when the y-intercept is not an integer):
y - 4 = -1/3 (x +2)
Have the student pairs transform this to slope-intercept form to highlight the fact that the y-intercept is a fraction, and thus it is impossible to accurately plot the graph (both because of the y-intercept and because of the impossibility of using the graphical definition of slope to find a second point on the line).
Finally, pass out the attached handout and have student pairs practice gathering information from the two forms of equation.