Foundations

Table Regression on the SAT: Desmos Walkthrough

Plot the two given points in Desmos, draw the straight line through them with one point-slope line, and evaluate it at any

x

to read the answer.

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 shows two values of $x$ and their corresponding values of $y$ . In the xy-plane, the graph of the linear equation representing this relationship passes through the point $(\frac{1}{7}, a)$ . What is the value of $a$ ?

$x$	$y$
$negative 18$	$negative 48$
$7$	$52$

$- \frac{4}{11}$

$- \frac{4}{77}$

$\frac{4}{7}$

$StartFraction 172 Over 7 EndFraction$

How to solve it in Desmos, step by step

The idea

Plot the two table points so Desmos draws the line through them, then evaluate the line at x equal to 1 over 7 to read the value of a.

1
Step 1
Type this to plot the first table point. A dot appears at negative 18 and negative 48.
Type in Desmos
$\left(-18,-48\right)$
2
Step 2
Type this to plot the second table point. A dot appears at 7 and 52.
Type in Desmos
$\left(7,52\right)$
3
Step 3
Type this point-slope line through both points. Desmos draws the line and you do not need to solve the slope yourself.
Type in Desmos
$y=-48+\frac{52-\left(-48\right)}{7-\left(-18\right)}\left(x-\left(-18\right)\right)$
4
Step 4
Type this to evaluate the line at x equal to 1 over 7. Desmos shows 172 over 7, about 24.571, which is choice D.
Type in Desmos
$f\left(\frac{1}{7}\right)=-48+\frac{52-\left(-48\right)}{7-\left(-18\right)}\left(\frac{1}{7}-\left(-18\right)\right)$

The answer is D.

$StartFraction 172 Over 7 EndFraction$

Now you try one

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

The table shows two values of

x

and their corresponding values of

y

. In the

xy

-plane, the graph of the linear equation representing this relationship passes through the point

\left(\frac{1}{5}, a\right)

. What is the value of

a

$x$	$y$
$-12$	$-30$
$8$	$50$

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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Table Regression on the SAT: Desmos Walkthrough

A real SAT-style question

How to solve it in Desmos, step by step

The idea

Step 1

Step 2

Step 3

Step 4

Now you try one

Practice this with a live Desmos calculator

More Desmos SAT lessons