Your Algebra student is probably like most who don’t have enough time to learn how to use a TI-84 Plus graphing calculator.
That’s because teachers are under a time crunch to teach the standards within a pacing guide. Every day needs to be content-focused. There’s just not a lot, if any, time to teach students about math tools. So teachers are teaching students how to do the work long-hand.
But knowing how to properly use the graphing calculator can:
- Produce faster, more strategic, and more efficient work on standardized testing
- Cut down on computation errors
- Build confidence to use the calculator for higher-level math
It all starts with learning the basics of how to graph.
This article is a clear step-by-step guide to walk you through how to make a graph, plus how to find the x- and y-intercepts.
How to Graph a Linear Equation Using a TI-84 Plus Graphing Calculator
1. Make sure your linear equation is in y = mx + b form (also called slope-intercept form)
Here’s the thing: students MUST input in this form. The TI-84 Graphing Calculator is designed to only accept equations in a form that has an isolated “y” value.
The sleek, new TI-Nspire allows the luxury of graphing from any form. But again, it’s not necessary. Plus, most school districts can only afford class sets of the TI-84s for their students. So it’s best to learn how to use the 84s.
2. Press the [Y= Button] on the top left of the calculator. When you press the button, your screen will change to a vertical list of “y=”.
3. Type in your equation, excluding the “y=” part. Be careful. This may sound pretty simple, but students can easily make mistakes here.
Helpful Hint: If your slope is a fraction, make sure it is contained in parentheses. Instead of just typing out:
3/2x + 4
you should type
(3/2)x + 4
Make it a habit of typing in the calculator this way.
Students mistakenly trust the calculator to perform the actions I told it to accurately. But the actions weren’t accurate.
Switching (3/2)x with 3/2x, where the x is in the denominator makes a totally different looking graph.
Be careful with small errors. The calculator is built to calculate using the Order of Operations. But the calculator does what the person puts in, so the calculator can produce errors if the user makes mistakes.
4. Press the [Graph] button. This creates a coordinate plane, typically with 10 tick marks up, down, left, and right on the x and y axes.
5. Adjust your window, if needed, by pressing the [Window] button. The window can be zoomed in or out by changing the x and y values.
Reasons to adjust the window:
- Nothing shows up on your screen: You know you put in an equation and pressed the Graph button, but the screen is blank.
- Only part of the graph shows up: You can see some of your graph, but you’re missing some key features, like the intercepts.
- You can’t tell what you are looking at: You see your graph and your key features, but that’s all.
How to Find the x-intercept
The TI-84 graphing calculator can help you identify the x-intercept in a linear equation.
In longhand, the student would need to substitute 0 for “y” in the equation, then solve for “x”.
The calculator is a better choice to find the x-intercept when:
- You are already instructed to graph your linear equation or
- You also need more information about the graph (key features)
But finding the x-intercept is not just graphing your equation and seeing where it crosses the x-axis.
True, you can do that and get a pretty good idea of what the x-intercept is. But that only works if the graph crosses the x-axis directly at a tick mark.
All equations won’t always be so neat and tidy, though.
If the graph crosses the x-axis anywhere other than a tick mark, you’re simply guessing where you think it’s going to cross. It’s not exact.
And guessing isn’t enough.
This is why I see so many students spend time graphing linear equations AND spend more time calculating the x-intercept by hand. It’s a waste of valuable time.
Those students don’t understand that the graphing calculator can also tell them the exact x-intercept.
Look at this example below.
y = 5x – 4
It makes a graph that looks like this:
Now, say the instructions call for you to find the x-intercept. You see that the graph is not directly crossing over the tick mark.
Here’s what you do:
Press the [2nd] button, then press the [Trace] button on the top next to the [Graph] button.
This is called the “Calculate” feature.
This feature has a whole list of uses, from maximums and minimums on quadratics to solutions of systems of linear equations.
For our this problem, we will select “zero.”
When we do, we will see our graph again. But this time, “Left Bound?” shows up at the bottom of our screen. A blinking cursor also shows up.
You can use the left and right arrow keys to move the cursor up or down the graph.
Since the Calculator is asking for your “Left Bound,” move your cursor somewhere on the left side of your x-intercept and press [Enter].
Now it’s asking for the “Right Bound.” Move your cursor to the right side of the x-intercept and press [Enter] again.
The Calculator’s last prompt is “Guess.”
For this one, move your cursor close to where you see your x-intercept and press [Enter].
After that, the bottom of the screen will say “Zero: X = .8 Y = 0” from our example.
And there you go.
Those will be the coordinates of your x-intercept.
No paper and pencil needed.
How to Find the y-intercept
You can also find the y-intercept of a linear function using the graphing calculator.
However, if your equation is in “y = mx + b” form (slope-intercept form), you don’t need to find your y-intercept.
That’s because the y-intercept is the “b” value in your equation.
In our example equation of “y = 5x – 4”, the y-intercept is “-4” since this particular equation is in slope-intercept form already.
If you ever need to find y-intercept or any y-value, type in your equation with the [Y=] button. Then, press the [2nd] and [Trace] buttons again for the Calculate feature.
To find the y-intercept, select the “Value” function by pressing [Enter]. If you remember, we selected the “Zero” function to find the x-intercept. Be careful not to mix up the two.
The graph of the function will show up. At the bottom of your screen, you will see “X=” with a flashing cursor. That’s the area for you to type in a value.
To find the y-intercept, type “0” here and press [Enter]. It will display what your y-value is when x is 0, or the y-intercept.
Knowing how to use it to solve and graph a linear equation by hand is still important. But knowing how to take advantage of the graphing calculator important, too.
Beginner Algebra students just need to get over the initial intimidation and first understand the graphing calculator is a valuable math tool that’s worth the time to learn how to use.
I’ve taught high school Algebra for years and I see students struggle with the same things. Students have trouble remembering where to go, what to type, and what to press.
That’s easily solved with training and hands-on practice.
Strict pacing guidelines keep a lot of teachers from doing this with their students.
It’s tricky because an Algebra course builds on itself. Students may not yet have the content knowledge when going over the graphing calculator.
The calculator is used in so many units that graphing calculator training would have to be taught every time there’s a new unit.
Plus, all the graphing calculator functions can’t be taught in one class period, not with a roomful of beginner students.
Some teachers may set aside calculator training until all content has been taught. That way, students have the content knowledge and it actually helps speed up the review time for end-of-course standardized testing.
Even with those obstacles, knowing how to use the calculator is definitely necessary.
Do your own research, if you aren’t getting calculator training in class. And get additional help if you need it.
It’s worth it.