Even the best mathematicians need ways to check their work. We’re going to use the graphing calculator to make sure we have the correct answer.

Below is a typical question related to slope-intercept.

Example

Which equation best describes the following graph?

Graph, x's and y's increasing, y-intercept (0,5); A. y=-3/4x+5, B. y=-4/3x+5, C. y=3/4x+5, D. y=4/3x+5

Interactive popup. Assistance may be required.

Check Your Answer

From your practice you probably know that the y-intercept is 5 and the line goes up 3 and right 4.

The answer is C y = 3 over 4 3 4 x + 5.Close Pop Up

If you are not sure of the answer, you can use your calculator three different ways to double check. You should learn all three methods because there will be times when one of the methods will not be obvious.

Method 1: Match the Graph

Calculator image of equation and graph of y=3/4 x+5

Interactive popup. Assistance may be required.

Check Your Answer

The graph on the calculator looks similar to the given graph but I can’t be sure.  I certainly can tell the line is increasing. A and B are definitely wrong.
A y = 3 over 4 3 4 x + 5

B y = 4 over 3 4 3 x + 5 Close Pop Up

Method 2: Match the Graph to the Table

Calculator image of equation and table of values for y=3/4 x+5

Interactive popup. Assistance may be required.

Check Your Answer

I found two points on the line in the table. I’m certain I’m correct. But why not try another check?Close Pop Up

Method 3: Match Points on a Graph Using TRACE

Calculator images: equation y=3/4 x+5; graph y=3/4x+5; Line graph, points (0,5), (4,8), (-4,2), (-8,-1), line going down with y-intercept at -2

Press the TRACE button and type -4 and press ENTER.

Interactive popup. Assistance may be required.

Check Your Answer

Close Pop Up

Repeating this procedure, with the graph on the calculator screen, press the TRACE button and type in - 8 and press ENTER.

Interactive popup. Assistance may be required.

Check Your Answer

Close Pop Up

Now I’m really satisfied I got the correct answer.

Which of the following equations best describes the graph shown below? Double check your answer using all three methods.

The answer is D because the y–intercept is -2 and the line goes down 1 and right 4.

Here is how you can be 100% certain:

Method 1: Match the Graph

Calculator image: equation and graph of y=-1/4 x-2; Graph of y=-1/4 x-2 with four points

Graph is decreasing. This could be correct.

Method 2: Match the graph to the table.

Calculator image: equation and table of y=-1/4 x-2

Both points (0, -2) and (4, -3) are on the graph given. I’m pretty certain.

Method 3: Match Points on Graph Using TRACE

Calculator image graph of equation y=-1/4 x-2; Calculator image graph with point (8,-4)

The graph was close, the table matches points on the graph, and using the TRACE button checked two more points. I got this problem right!