Graphing
To begin graphing linear equations, you need to be able to graph points. Here is a quick review and an applet you can play with: http://mathforum.org
/cgraph/cplane/pexample.html
Now view the different forms of linear equations and how to graph them: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/EqLines2.htm
The most frequent form of a linear equation is y = mx + b. When an equation is in this form, (x, y) are the points on the line and for every x value there is a unique y value. We can also tell from this equation that m is the slope, and b is the y-intercept. The equation y = 4x + 2 has a slope of 4 and the y-intercept is 2. We can find the value of y when x = 1 by substituting in 1 for x:
y = 4(1) + 2
y = 6
The point on this line where x = 1 is (1, 6). To easily graph an equation in this form, find your y-intercept and place the point on the graph. Next, use your slope. Remember that slope is rise over run, so if the slope is positive you move up, if the slope is negative you move down. Count up or down the number of tics on the y-axis for the number that is in your numerator of your slope. Then count right the number in the denominator. So, for our above example of y=4x+2, the y-intercept is 2. Place a point at (0,2). The slope is 4. Count up 4 and then over 1, remembering that every whole number has a denominator of 1. There should be a point at (1,6). Connect those two points and you have the line y = 4x + 2.
/cgraph/cplane/pexample.html
Now view the different forms of linear equations and how to graph them: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/EqLines2.htm
The most frequent form of a linear equation is y = mx + b. When an equation is in this form, (x, y) are the points on the line and for every x value there is a unique y value. We can also tell from this equation that m is the slope, and b is the y-intercept. The equation y = 4x + 2 has a slope of 4 and the y-intercept is 2. We can find the value of y when x = 1 by substituting in 1 for x:
y = 4(1) + 2
y = 6
The point on this line where x = 1 is (1, 6). To easily graph an equation in this form, find your y-intercept and place the point on the graph. Next, use your slope. Remember that slope is rise over run, so if the slope is positive you move up, if the slope is negative you move down. Count up or down the number of tics on the y-axis for the number that is in your numerator of your slope. Then count right the number in the denominator. So, for our above example of y=4x+2, the y-intercept is 2. Place a point at (0,2). The slope is 4. Count up 4 and then over 1, remembering that every whole number has a denominator of 1. There should be a point at (1,6). Connect those two points and you have the line y = 4x + 2.
_Still
confused? Watch some videos. First we'll graph an equation using
slope-intercept form, then we'll graph using intercepts and/or points on
the line. You can always use any of these methods to graph.
If the videos are not working, you need to download the Adobe Flash player.
If the videos are not working, you need to download the Adobe Flash player.
PRACTICE
Now use this interactive guide to see how changing the slope and y-intercept changes the line. What happens when the slope is negative? When the slope is 0? What about when the y-intercept is negative or 0? http://enlvm.usu.edu/ma/nav/activity.jsp?sid=__shared&cid=emready@eqns_lines&lid=4 Note any observations in the Interactive Activities forum below.
ASSESS
Try this interactive quiz: http://teachers.henrico.k12.va.us
/math/HCPSAlgebra1/Documents/examviewweb/ev5-4.htm
Now test yourself: http://www.math.com/school/subject2/practice
/S2U4L3/S2U4L3Pract.html. Post your score in the forum below.
Once you have mastered graphing, move on to graphing inequalities.