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Basic Algebra

Basic Algebra

At a Glance - Graphing Lines by Plotting Points

Most of the lines you will be graphing will much more complex than simple vertical and horizontal lines. There are many ways to go about graphing these, but we will only work with the two most common methods: plotting points and slope-intercept form.

Graphing lines by plotting points is pretty simple. Just find two or more points - any (x,y) points - on the line and connect the dots.

Although you really only need two points to make a line, finding a third one is often a good idea. If all three points lie in a straight line, you can feel confident that you didn't make a mistake. If the third point doesn’t fit your line, check your work and try again.

Let's start with a simple example:

y = 2x + 1

To find three points on this line, pick any values you want for one variable, plug them into the equation, then solve for the other variable.

Since y is already isolated in this equation, it would be a good idea to start by picking values for x. This will give you a value for x and one for y; an (x, y) point!

Here’s a tip: in the beginning, go easy on yourself and pick nice and simple values for x, like -1, 0, and 1.

Pick an x valuePlug into y = 2x + 1Solve for y(x, y)
0y = 2(0) + 1y = 2(0) + 1

y = 0 + 1

y = 1
1y = 2(1) + 1y = 2(1) + 1

y = 2 + 1

y = 3
-1y = 2(-1) + 1y = 2(-1) + 1

y = -2 + 1

y = -1

Now that we have our three points, we can plot these on a coordinate grid and connect.

graph 5

Look Out: although you can graph a line by only plotting two points, it is always a good idea to do at least three. If all three lie in a straight line, you can feel pretty confident that your answer is correct.

Example 1

Graph the equation y = -½x – 2.

Example 2

Graph the equation x + 3y = 7.

Example 3

Graph the equation 2y = 6x.

Exercise 1

Graph the lines y = ½ and x = -½ on the same coordinate grid.

Exercise 2

Graph the line: y = 4x – 3.

Exercise 3

Graph the line: 5x + 10y = 25.