Question 43·Easy·Two-Variable Data: Models and Scatterplots
The table shows paired values of two variables, and .
| 1 | 3 |
| 3 | 7 |
| 5 | 11 |
| 7 | 15 |
Which of the following is closest to the slope of the line of best fit that models as a function of ?
For questions asking for the slope of a line of best fit from a table or scatterplot, pick two clear points that lie on or very close to the trend line—ideally the ones farthest apart to reduce rounding error. Compute the slope as (here, ), simplify the fraction, then choose the answer option that matches or is closest to that value. Avoid common mistakes like flipping the ratio or ignoring how much the horizontal variable changes.
Hints
Think about what the slope measures
The slope of a line of best fit tells you how much changes, on average, when increases by 1. How can you compute that from two points?
Use two points from the table
Pick any two points from the table (for example, the first and the last) and calculate the change in and the change in between them.
Form the slope as a fraction
Once you have and , form the ratio and simplify it. Then see which answer choice is closest to that value.
Desmos Guide
Enter the data into a table
In Desmos, add a table. Enter the values (1, 3, 5, 7) in the column and the corresponding values (3, 7, 11, 15) in the column.
Perform a linear regression to get the slope
In an empty line, type y1 ~ m x1 + b. Desmos will display values for m and b; m is the slope of the line of best fit. Compare this m value to the answer choices and select the choice closest to it.
Step-by-step Explanation
Recall what the slope represents
For a line (or line of best fit), the slope is the rate of change:
- Slope change in divided by change in , often written as .
- You can use any two data points from the table to compute this, especially ones that are far apart.
Choose two points and find the changes
Pick two points from the table, for example and .
- Change in : .
- Change in : .
So the (unsimplified) slope is
Simplify the slope and match the answer choice
Now simplify the fraction from the previous step:
This value is the slope of the line that models as a function of , so the closest answer choice is .