Skill: Use a line of best fit to make predictions

A line of best fit shows the overall trend in a scatter plot. It can be used to estimate one variable when the other variable is known.

Worked example

A scatter plot compares the number of hours students study, $x$, with their test score, $y$. The data points show a generally increasing trend, so a line of best fit is drawn.

Suppose the equation of the line is

$$y=6x+52.$$

Estimate the test score for a student who studies for $6$ hours.

Step 1: Identify the known value

The number of study hours is known:

$$x=6.$$

Step 2: Substitute into the line equation

Replace $x$ with $6$:

$$y=6(6)+52.$$

Step 3: Calculate

$$y=36+52=88.$$

Step 4: State the prediction

The predicted test score is approximately

$$\boxed{88}$$

So, a student who studies for $6$ hours is expected to score about $88$.

The prediction is approximate because the actual data points do not all lie exactly on the line. A prediction made within the range of study times shown in the scatter plot is usually more reliable than one made far beyond that range.