GED Graphing and Functions: 25 Practice Questions on Slope, Lines and f(x)

If graphs make your eyes glaze over, you’re not the only one. Most people haven’t drawn one since school.

But you already read one kind of graph every month: your phone bill. There’s a flat fee, plus a little more for each thing you use. Put that on a grid and you get a straight line.

The catch? On the test, the wrong answers look almost exactly like the right one. If the slope is 2/3, you’ll also see 3/2 and −2/3. Knowing what each number means is how you tell them apart.

On this page you’ll get:

• 25 practice questions (scroll up), new ones every time
• Slope, explained with a phone bill
• How to read a line off a graph in seconds
• What f(x) means (it’s less scary than it looks)

Skills in this set: Slope from two points · Plotting points on the coordinate plane · Slope from a graph · Slope from a table of values · Writing a linear equation from a description · Finding intercepts from an equation · Matching a graph to its equation · Identifying a point on a line · Plotting a point from an equation · Evaluating functions in function notation · Reading function values from a table · Comparing linear functions in different forms · Recognizing a function from a table · Unit rate as the slope of a proportional relationship · Interpreting slope and intercept in context · Solving a system of equations by graphing · Deciding whether a table is linear · Writing the equation of a line through two points

What graphing questions look like, starting with a phone bill

Graphing on the GED is mostly straight lines and what they mean. You’ll get a line on a grid, a table, an equation or a short story. Then you’ll be asked for the slope, the starting value, the equation, or which of two plans costs more.

Start with the phone plan: $45 a month, plus $6 for each extra gig. With no extra gigs you pay $45. With 1 you pay $51, with 2 you pay $57, and every extra gig adds the same $6.

That $6 is the slope. Slope is how much the line goes up for each step across. On the grid, each step to the right (one more gig) takes the line up 6 (six more dollars).

The $45 is the starting value, called the y-intercept. It’s where the line begins on the left edge of the grid, when you’ve used 0 extra gigs.

Put them together and you get y = 6x + 45. That’s the y = mx + b on the formula sheet. The m is the amount that repeats (the $6), and the b is the amount you pay once or start with (the $45).

To read a line off a graph in seconds, find two points where it crosses a grid corner exactly. Count up or down first, then across. Up over across is the slope, and if the line falls as you move right, the slope is negative.

Then look where the line crosses the up-and-down axis (the y-axis). That number is b. With m and b, you can write the equation or spot it among the choices.

Now for f(x). It looks scary, but it’s just a name for a rule. Think of the phone plan as a machine: you feed in the number of gigs, and it hands back the bill.

So if f(x) = 6x + 45, then f(3) means “the bill when x is 3”. Put 3 wherever x appears: 6 × 3 + 45 = $63.

The test also asks about parallel and perpendicular lines, whether a table is a function, and where two lines cross (the point where two gym plans cost the same). Some items ask you to click on the grid to plot a point.

Counting a slope off a grid or finding f(−2) needs only small whole numbers, so these could show up in the first five or so questions, which have no calculator.

How many questions? This topic is its own scoring area, worth about 25% of the test. There’s no official count, but on about 46 questions that’s roughly eleven or twelve by our math, so practice here pays off.

The topics and area weights come from GED Testing Service’s official test guide. It doesn’t publish a question count per topic, so any count here is our estimate.

The 4 mistakes that cost the most points

Each wrong answer in the practice set is the result of one specific slip, and the explanation names it. These are the ones that come up most in this topic.

One problem, worked out step by step

How to get better at this, fast

1. Pick two points where the line crosses a grid corner exactly. Count squares up or down first, then across, and put the up-or-down count on top.
2. With the slope formula, write the two points one above the other and subtract in the same order top and bottom, even when the numbers are small.
3. Read f(3) as “the output when the input is 3”. Put parentheses around the input before you substitute, so 2x² − 5 at x = −3 becomes 2(−3)² − 5.
4. To compare two plans shown in different ways, turn both into a rate first. Divide the table’s change in y by its change in x, write it next to the m from the equation, then compare.