Worked examples
The questions the video works, written out: the setup, each step, the answer and the trap.
0:43Example 1
A scatterplot shows hours studied on the x-axis and test score on the y-axis for a group of students. The line of best fit is . What does the slope represent, and what does the y-intercept represent?
- The line is in slope-intercept form, y = mx + b, so read m = 5 and b = 45 straight off the equation.
- Slope is change in y per one unit of x. Here y is score and x is hours, so the slope 5 means the predicted score rises 5 points for each additional hour of study. It is a rate, points per hour.
- The y-intercept is the value of y when x = 0. Substituting x = 0 gives , so 45 is the predicted score for a student who studied zero hours.
- Check the rate: from x = 2 to x = 3 the line goes from 55 to 60, a rise of exactly 5.
Answer: slope: about 5 points per hour of study; y-intercept: a predicted score of 45 with no study
Slope always carries the units of y over the units of x, points per hour, which is why it reads as a rate and not as a score. The trap is describing the slope as a single score, or describing the intercept as the first plotted point; the intercept is where the line crosses x = 0 whether or not a dot sits there, because the line balances the cloud rather than passing through any particular dot.
1:13Example 2
Using the line of best fit , what score does the model predict for a student who studies 6 hours? Is that an interpolation or an extrapolation?
- Do not hunt for a dot at x = 6. The line is the model, so substitute x = 6 into its equation.
- .
- Six hours sits inside the range of hours that were actually plotted, so this is an interpolation, a prediction within the data.
- Check: 75 - 45 = 30, and 30 divided by the rate of 5 points per hour is 6 hours.
Answer: 75, an interpolation
The line summarizes the trend, so plugging x into its equation gives the model prediction even when no student studied exactly 6 hours. The trap is reading the nearest dot instead of the line; individual dots sit above and below the line, and the question asks what the line predicts.
1:40Example 3
Using the same line of best fit, , predict the score after 10 hours of studying. Is that prediction an interpolation or an extrapolation?
- Substitute x = 10: .
- No plotted student studied as long as 10 hours, so 10 lies beyond the data. That makes this an extrapolation.
- An extrapolation assumes the trend keeps going past anything measured, so it is the line making a claim rather than an observation; the question asks what the line predicts, and the line says 95.
- Check: from 6 hours to 10 hours is 4 more hours, and 4 times 5 points is 20, which carries the earlier 75 up to 95.
Answer: 95, an extrapolation
Same move as before, substitute and compute, but the label changes because x = 10 is outside the plotted range. The trap is calling it interpolation because the arithmetic feels identical; interpolation stays inside the data, extrapolation reaches past it. A second trap is adding 5 once to the highest score seen instead of using the equation.
Lesson transcript
The narration of the video, word for word, under its chapter headings.
Welcome to SAT Climb. A scatterplot is a cloud of dots — and the SAT wants you to find the one line that captures the trend, then use it to predict scores you can't even see on the graph. A scatterplot plots two variables — here, hours studied vs score. Each dot is one data point. They trend upward, but don't line up perfectly, so we summarize them with one straight line. That line is the line of best fit. It balances the dots — some above, some below — modeling the trend, not any single point. Its slope is the rate: each extra hour adds about 5 points. Its intercept, 45, is the score at 0 hours. So the model is y = 5x + 45. Now the payoff: prediction. Don't hunt for a dot — plug an x into the equation. After 6 hours, y = 5(6) + 45 = 75. Predicting inside your data is interpolation; reaching far beyond is extrapolation — safe only if the trend holds. Your turn. Use the line to predict the score after 10 hours. 5(10) + 45 = 95. And since 10 is past our data, that's an extrapolation. Three traps. One: the best-fit line balances the dots — it doesn't hit them all. Two: slope is a rate — points per hour, not a score. Three: the intercept is the value at x = 0, where the line crosses — not the first dot. Scatterplots: solved. Fit the line, read its slope as the rate and its intercept as the start, then predict. Start your free trial at satclimb.com. Keep climbing.
Read the written version: the Two-variable data: models & scatterplots strategy guide, then try 25 hard Two-variable data: models & scatterplots questions with full explanations. Both are free, no account needed.