Graphing Linear Equations Worksheet

Most graphing practice starts with an equation and asks students to plot it. This worksheet flips the order. It opens with a decision students will actually face — which bank checking account costs less — and lets the linear equation grow out of that decision instead of being handed down first.

The setup is a fee comparison between two checking accounts, each with a different monthly maintenance fee and a different out-of-network ATM charge. Framed correctly, each account is a linear equation: a fixed monthly cost (the y-intercept) plus a per-use charge (the slope) times the number of ATM withdrawals. Before students touch a graph, they have to reason through which account wins under different usage patterns, and whether "better" even has one answer. It doesn't, and that's the point — question 2 pushes students to name the factors that flip the comparison.

Once that groundwork is laid, the worksheet moves into direct graphing practice: identifying slope and y-intercept from a set of equations, plotting the y-intercept, and using the slope to place additional points. It's straightforward mechanical practice, but it lands differently after students have just spent three questions reasoning about what slope and y-intercept mean in a real account.

This pairs naturally with a unit on banking basics or account fees, and works as a bridge between a "why do we graph lines" discussion and a pure skills-practice day. It assumes students already know what slope and y-intercept are; if they don't, save this for after that lesson.

The banking scenario also has staying power beyond this one lesson. Most students will open a checking account within a few years of sitting through this worksheet, and out-of-network ATM fees are exactly the kind of small, recurring cost that adds up quietly if nobody ever taught you to compare it against a fixed monthly fee. Framing the graphing practice around a decision they'll actually make gives the skill a reason to stick instead of fading the way isolated equation drills tend to. Below is the worksheet exactly as it appears in Rapunzl's curriculum, ready to assign as-is or adapt for your classroom.

This worksheet comes from Module 14 of Rapunzl's financial literacy curriculum, part of the Financial Equations unit that connects algebra to the kind of financial decisions students will actually run into.

Graphing Linear Equations

Many banks charge for out of network ATM use. Out of network ATMs are ones provided by someone other than your bank. While you’re away at college, you will have to rely on these out of network ATMs if your local bank does not have a branch near your school. Compare the following checking account fee structures.

1. Which bank offers a better fee structure for a month of usage? Describe your reasons.

 

1. Is one bank ALWAYS better? What factors might affect which bank has the better fee structure?

 

1. How could you avoid these fees if you are away at school without access to a local branch?

 

1. Practice Drawing Equations On Graphs

Use a separate sheet of paper to plot the remaining equations below. First, identify the slope and y-intercept for each of these equations. Then plot the y-intercept and use the slope to plot additional points.

A.

B.

C.

D.

E.

F.

G.

H.

I.

Teacher Notes

Questions 1 through 3 are the heart of this worksheet, and they're deliberately open-ended. There is no single correct answer to "which bank is better" — it depends on how many out-of-network withdrawals a student makes in a month. Students who plug in a specific number of withdrawals and compare totals are doing real algebra, even if they never write an equation with a variable. Let that reasoning surface before you introduce the formal linear equation for each account.

Question 3 is a practical financial literacy check as much as a math question. Look for answers involving cash-back at point of sale, in-network ATM locators, or online banks with no ATM network at all — all valid ways students might avoid the fee structure entirely rather than optimizing between the two options given.

Item 4 is standard graphing practice: identifying slope and y-intercept from an equation and plotting from there. Since students supply their own paper for this part, it's a good candidate for a quick partner check or a document camera walk-through once most students have finished, rather than individual grading. If a student finishes early, have them plug their own realistic monthly withdrawal count into both bank equations and check that the graph agrees with whichever total they calculated back in question 1 — it's a fast way to confirm the graphing and the reasoning line up.

This activity is one piece of the full Financial Equations unit inside the Rapunzl teacher portal, sequenced with guided notes, slides, and additional graphing practice that builds on slope and y-intercept.

Want the rest of the Financial Equations unit, plus the tools to run it in your classroom? Book a Rapunzl demo and see how students connect algebra to real financial decisions.