A drawn line of best fit models the trend, while individual scatterplot dots may miss it. When every coordinate changes by the same rule, convert a labeled point on the line, then use Desmos to test that new point in the choices. Watch the order of the changes: subtracting before dividing is different from dividing before subtracting.
Hints
- Hint 1
An open circle on the line of best fit gives a point on the model. A filled dot is an observed measurement and might not lie on that line. Which labeled point could you convert?
- Hint 2
The new -coordinate is half of what remains after subtracting from the old -coordinate. How would you write that as one expression?
- Hint 3
A choice must give the transformed point’s -coordinate when you enter its new -coordinate. Test each right side at that input.
Step-by-step
Transform a point on the fitted line
Step 1Translate the coordinate changes
Write for an old point and for its new coordinates. The directions become . The rule says subtract before dividing; would reverse the order.
- Step 2
Convert a point on the line
The open circle lies on the fitted line; a filled scatterplot dot need not. Type and in Desmos. It shows and , so becomes . A point on the fitted line transforms with the line.
- Step 3
Test the transformed point
Type the four choices’ right sides with in Desmos. In order, Desmos shows , , , and . Only the first gives , the -coordinate the new line needs at . So a line of best fit for data set H could be . Choice A.