Graphing Linear Equations

Every week, thousands of students ask our tutors for help with homework or studying with tests. We took a look at the most popular question over the past week in Algebra and realized that a lot of students are struggling with graphing linear equations. We can help!

For example, let’s say you have to “Graph the equation 2x – y = -4

Let’s go through the steps to get the right answer.

The first thing you need to do is to make sure you understand the Key Terms.

Key Terms:

Variable: any letter in an equation (x and y in our problem)

Coefficient: the number in front of the variable; if no number is shown we assume it to be 1. In the above equation the coefficient of x is “2” and the coefficient of y is “1”.

Constant: a number by itself with no variable attached to it, in our equation the constant is “-4”

Solution:

Step 1: Rewrite the equation into the general formula y=mx+ b. (This is called the slope-intercept form).

Note:  It doesn’t matter if the y is on the left or the right, it will solve the same way.  The key part is to not lose a minus sign.

2x – y = -4
___+y         + y

2x = -4 + y

2x      = -4 + y
+ 4    +4

2x + 4 = y

Step 2: There are two ways to solve this kind of problem. You can either make a table of points (also called a T-chart) or by using the slope and y-intercept. Check with your teacher, notebook or textbook to see which your class uses.

To solve with a table of points, we need at least 2 points to make a line.  The easiest ones to use are the ones where we put 0 in for x and solve for y and then repeat by putting 0 in for y and solving for x.

So let x = 0, we get….    2 (0) + 4 = y
0 + 4 = y   so our first point is (0,4)

Now let y = 0, we get…  2x + 4 = 0
2x + 4 –4 = 0-4 (subtract 4 from both sides)
2x = -4

2x = -4 (divide both sides by 2)
2        2
x = -2      so our second point is (-2,0)

The table would look like this:

x y
0 4
-2 0

To solve using the slope and y-intercept, now that we have the equation in the form y = 2x +4, this is equivalent to the general y = mx + b, where the m (the coefficient/number) with the x is the slope and the b (number by itself) is the value of the y-intercept.

So the point we have is (0, 4) and the slope is 2.  Slope is defined as rise/run and we’ll use 2/1 for our slope when we make the graph.

Step 3: Graph the equation.

To make it easier to visualize, we’ve used the Tutor.com classroom to demonstrate. If you are doing this without our online tutors, you can use graph paper and pencil.

Create a quadrant on your graph paper.

To graph using the table, we have 2 points (0, 4) and (-2, 0) to put on our graph.  For the first one, the x value is 0, so our point will be on the +y-axis at a value of 4.  Make your point on the graph (here it’s a blue dot).

Next plot the other point, (-2, 0); this time it will lie on the – x-axis (to the left) like this (red dot).

Now we add in the line.

To graph using the slope and a point, start the same way with graph paper and the coordinate axes.

Next plot the point (0,4) on the + y-axis as shown below (the blue dot).

Slope is defined as rise/run, which means we can either count up 2 squares and 1 square to the right (2/1) or, we can count down 2 squares and 1 square to the left (-2/-1) to show where our next point would be.

We hope that helped! Remember, you aren’t alone. Linear equations can be confusing for even the most dedicated student. If you need more help, don’t hesitate to connect to a tutor at Tutor.com.

2x = -4 (divide both sides by 2)

2       2

x = -2        so our second point is (-2, 0)

One Response to Graphing Linear Equations

  1. Anonymous July 23, 2010 at 10:08 PM #

    I can definitely see the advantage, in this example, of having access to the tutor.com classroom. Graphing on paper can be sloppy and really distracts the student from the lesson being given. I think that anyone wanting to be a tutor today should really take advantage of the technology available. And thank you, tutor.com, for another good teaching example.
    Peggy

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