Foundations

Table to Function on the SAT: Desmos Walkthrough

Plot the table's points in Desmos, then graph each answer choice and keep the one whose line passes through both dots.

This is a Foundations lesson: the core Desmos moves (graphing both sides, plotting points, reading intersections) that every other technique in the course builds on.

Take this lesson interactively

A real SAT-style question

The table gives the number of hours, $h$ , of labor and a plumber’s total charge $f (h)$ , in dollars, for two different jobs.

There is a linear relationship between $h$ and $f (h)$ . Which equation represents this relationship?

$h$	$f (h)$
$1$	$155$
$3$	$285$

$f (h) = 25 h + 130$

$f (h) = 130 h + 25$

$f (h) = 65 h + 90$

$f (h) = 90 h + 65$

How to solve it in Desmos, step by step

The idea

Only two points are given, so the fastest way is to plot both points, then graph the answer choice and check the line passes through both dots.

1
Step 1
Type this to plot the two points from the table: 1 hour costs 155 dollars, and 3 hours costs 285 dollars. Two dots appear on the graph.
Type in Desmos
$\left(1,155\right)$ $\left(3,285\right)$
2
Step 2
Type the equation from choice C. A straight line appears on the graph.
Type in Desmos
$f=65h+90$
3
Step 3
Look at the graph. The line passes through both dots, so choice C is correct: f equals 65 times h plus 90.

The answer is C.

$f (h) = 65 h + 90$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

The table gives the number of hours,

m

, of labor and an electrician's total charge

g(m)

, in dollars, for two different jobs. There is a linear relationship between

m

and

g(m)

. Which equation represents this relationship?

$m$	$g(m)$
2	190
5	310

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

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