Question type

Line of best fit questions on the SAT

A line of best fit $y = m x + b$ predicts $y$ from $x$ . The slope $m$ is the predicted change in $y$ for each increase of 1 in $x$ , in the units of the context; $b$ is the predicted value when $x = 0$ . A point above the line is an actual value greater than the prediction.

These questions use a scatterplot's line of best fit to make a prediction, compare an actual data point with the predicted value, count points above or below the line, or interpret the slope or intercept in words.

It appeared on three of the five official practice tests we analysed.

On 3 of 5 official practice tests
27 practice questions of this type
Desmos partly helps

Why students miss it

Getting the direction of the slope wrong: $- 1.8$ means the value decreases as age increases.

Forgetting the units. If $y$ is in thousands of dollars, a slope of 1.8 means 1,800 dollars.

Reading "predicted" as "actual". The line gives a prediction; the dots are the data.

How to spot it

A scatterplot with a line drawn through it, or an equation called "the line of best fit".
"Best interpretation of" a number in the equation.
"Predicted", "estimated", "how many points lie above the line".

The method

Use or interpret the line

Name what $x$ and $y$ stand for, with their units.

Interpret the slope: change in $y$ per 1 unit of $x$ , with its sign.
Interpret the intercept: predicted $y$ when $x = 0$ .
Predict: substitute the $x$ value.
Above or below: compare the actual value with the line's value.

With Desmos

Desmos can draw the line and the points, but most of these questions are about meaning.

For a prediction, type the line, for example y=1.7x+5.2, and click it at x = 12.

Interpretation questions are answered by reading the context, not by graphing.

Two real questions

From the 1500prep bank, the way the app shows them. Answer first, then open the explanation.

1Question 1 of 2#800Data

The scatterplot shows the number of umbrellas sold at a shop on each of 8 days, along with the number of rainy hours recorded that day. The line of best fit for the data is given by $y = 3 x + 8$ . For how many of the 8 days was the actual number of umbrellas sold greater than the number predicted by the line of best fit?

Pick an answer, then check it.

Show the answer and explanation

Plug each x-value into y = 3x + 8 and compare. x=2: predicted 14, actual 15 (above). x=4: 20 vs 19 (below). x=5: 23 vs 25 (above). x=7: 29 vs 27 (below). x=9: 35 vs 37 (above). x=10: 38 vs 36 (below). x=12: 44 vs 46 (above). x=14: 50 vs 49 (below). Actual sales were higher than predicted on 4 days.

2Question 2 of 2#655Data

For a set of data relating the age x, in years, of a used car to its value y, in thousands of dollars, the line of best fit is y = 22.4 − 1.8x. Which of the following is the best interpretation of the number 1.8 in this equation?

Pick an answer, then check it.

Show the answer and explanation

The coefficient of

x

- 1.8

, so value drops

1.8

per extra year of age. Since

y

is in thousands of dollars, that's a decrease of

$1, 800

per year.

Questions students ask

How do you interpret the slope of a line of best fit?

As the predicted change in y for each one-unit increase in x, in the context's units. A slope of −1.8, with y in thousands of dollars, means the predicted value drops by 1,800 dollars per year.

What does a point above the line of best fit mean?

Its actual y-value is greater than the value the line predicts for that x.

Practise this type until it is automatic

Five more line-of-best-fit questions, checked instantly, with every wrong choice explained. Free, no card.

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