Lines and Slope || Chameleon Home || Ask Dr. Math

Graphing Points First

Often, you must use an equation to graph a line. For example, somebody might ask you to graph the line 4x + 2y = 8. When this happens, you have to find some points on the line before you can graph it.

Let's ask Joan to graph 2x + y = 6.

First, Joan needs to find values of x and y that make this equation true. She decides to let x = 0.

Now that Joan has chosen a value for x, she needs to find y, so she substitutes 0 into the original equation:

2x + y = 6
2*0 + y = 6
0 + y = 6
y = 6.

Joan has found that when x = 0, y = 6. She can graph this information as the point (0, 6):

If you need practice graphing points, visit Joan's brother, Sam.

Joan needs two points before she can graph a line, so she has to find another set of values for x and y. She decides to try making y = 0. This time, she substitutes 0 into her equation for y:

2x + y = 6
2x + 0 = 6
2x = 6
x = 3

Joan has found that (x = 3, y = 0) makes her equation true, so she graphs the point (3, 0).

Now that Joan knows where two points are, she can graph her line. She crawls up the y-axis until she reaches the first point, then sticks her tongue straight into the second point.

The straight part of Joan's tongue leaves a sticky green mark behind. She adds arrows to this line and labels it with her equation, then goes looking for a fly.

Joan has graphed 2x + y = 6.