Foundations

Basic Regression on the SAT: Desmos Walkthrough

Type the rule as a function, plot a couple of points one step apart, and read the change straight off their values.

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

$w (t) = 300 - 4 t$

The function $w$ models the volume of liquid, in milliliters, in a container $t$ seconds after it begins draining from a hole at the bottom. According to the model, what is the predicted volume, in milliliters, draining from the container each second?

$300$

$296$

$75$

$4$

How to solve it in Desmos, step by step

The idea

The line drops 4 each second because of the minus 4 in front of t. Plot two points one second apart and read the drop straight off the volume values.

1
Step 1
Type this first line to define the rule. Defining it alone does not draw anything yet, so add the two point lines next.
Type in Desmos
$w\left(t\right)=300-4t$
2
Step 2
Type these two lines. Desmos plots a point at height 300 for the first second and a point at height 296 for the next second.
Type in Desmos
$\left(0,w\left(0\right)\right)$ $\left(1,w\left(1\right)\right)$
3
Step 3
Read the two points. The volume falls from 300 to 296 in one second, a drop of 4 milliliters each second, so the answer is D) 4.

The answer is D.

$4$

Now you try one

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

p(t) = 500 - 7t

The function

p

models the volume of liquid, in milliliters, in a tank

t

seconds after it begins draining from an opening at the bottom. According to the model, what is the predicted volume, in milliliters, draining from the tank each second?

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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