Math

Scatterplots and Line of Best Fit

2 min readEasy5-question drill

Scatterplot questions are some of the most predictable points on the math section — once you know that the line of best fit is just `y = mx + b` in disguise, you can plug, read, and interpret your way to fast correct answers.

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→Two-Variable Data: Models and Scatterplots →Linear Functions →Linear Equations in 2 Variables

A scatterplot is a graph where each dot represents one data point with two measurements — like a student's hours studied (on the x-axis) and exam score (on the y-axis). When you plot lots of dots, you often see a general trend: maybe more studying tends to mean higher scores.

The line of best fit (also called the trend line or regression line) is a straight line drawn through the cloud of dots that comes as close as possible to all of them. It's the line that best summarizes the overall pattern. On the test, this line is almost always given to you as an equation:

y = mx + b

This is just the slope-intercept form you already know.

m is the slope — how much y changes for each 1-unit increase in x.
b is the y-intercept — the predicted y value when x = 0.

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Line of best fit y = 8.5x + 42: plug in x = 6 to predict a score of 93.

There are three things these questions ask you to do:

1. Predict a value. Plug an x into the equation and solve for y (or vice versa). If the line is y = 8.5x + 42 and you want the score for 6 hours, substitute x = 6.

2. Interpret the slope or intercept in context. The slope tells you a rate of change with units. If y is resale value in thousands of dollars and x is age in years, a slope of -2.3 means the value drops about $2,300 per year. The negative sign matters — it means y goes down as x goes up. The intercept b is the starting value when x = 0.

3. Describe the correlation. The correlation coefficient r measures how strongly the dots cluster around a line. It ranges from -1 to 1.

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Reading the correlation coefficient r

r value	Direction	Strength
+0.91	Positive	Strong
-0.85	Negative	Strong
+0.30	Positive	Weak
-0.12	Negative	Very weak / none

Sign sets direction; how close to 1 sets strength.

r near +1: strong positive relationship (dots rise left to right).
r near -1: strong negative relationship (dots fall).
r near 0: weak or no linear relationship.

A value like r = 0.91 is a strong positive correlation. One critical rule: correlation does not prove causation — two things trending together doesn't mean one causes the other.

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Quick check

A researcher collected data on the number of hours students studied and their exam scores. The line of best fit for the scatterplot is y = 8.5x + 42, where x is hours studied and y is the predicted exam score. What is the predicted exam score for a student who studied for 6 hours?

Worked examples

Example 1

A scientist plots the temperature (in °C) of a liquid versus the time (in minutes) it has been cooling. The line of best fit is y = -1.5x + 80, where x is time in minutes and y is temperature. What is the predicted temperature after 10 minutes?

Example 2

A real estate analyst models the relationship between a house's size (in hundreds of square feet, x) and its price (in thousands of dollars, y). The line of best fit is y = 15x + 90. Which statement correctly interprets the slope in context?

Example 3

A study records the daily hours of sunlight and the height (in cm) of 25 plants. The correlation coefficient is r = -0.12. Which of the following best describes the relationship between sunlight and plant height in this data?

Common pitfalls

Confusing slope with y-intercept

When asked about the rate of change, students sometimes grab b instead of m. The slope (m) is the per-unit change; the intercept (b) is the value when x = 0. Identify which one the question wants.

Ignoring the units of x and y

If x is in 'hundreds of feet' or y is in 'thousands of dollars,' a slope of 15 doesn't mean $15. Always translate the slope using the units defined in the problem.

Judging correlation by sign, not strength

A negative r isn't automatically 'strong negative.' Strength comes from how close |r| is to 1. r = -0.12 is weak; r = -0.88 is strong.

Assuming correlation means causation

A high r shows two variables move together, but it does NOT prove one causes the other. Reject any answer choice that claims X 'causes' Y based only on correlation.

Key takeaways

The line of best fit is just y = mx + b — slope m, intercept b.
To predict, substitute the known value and solve; to interpret slope, attach the real-world units of x and y.
A positive slope means y rises as x rises; a negative slope means y falls.
The correlation coefficient r runs from -1 to 1: magnitude = strength, sign = direction.
Correlation never proves causation.

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Try it yourself

5 practice questions on Scatterplots and Line of Best Fit, drawn from the question bank. The tutor is one click away if you get stuck.

Where this lesson fits

Scatterplots and Line of Best Fit

You are here

→Two-Variable Data: Models and Scatterplots →Linear Functions →Linear Equations in 2 Variables