Final answer:
Using the trend line y = 8x + 8 to estimate time is an example of linear regression estimation. It involves setting the distance to 5 miles in the equation and solving for time. However, the negative result suggests a misinterpretation or a problem with the equation's applicability.
Step-by-step explanation:
Using the trend line y = 8x + 8 to estimate how long it will take Yumiko to run 5 miles is an example of linear regression estimation. This linear equation represents the relationship between the distance Yumiko runs (y) and the time it takes (x). To calculate how long it will take Yumiko to run 5 miles, you would set y to 5 (5 miles) and solve for x. The solution will give you the time, in the same units used for x, that it would take Yumiko to run 5 miles, according to the pattern represented by this particular trend line.
The steps to solve this would be:
- Set y to 5 since that is the distance Yumiko wants to run.
- Plug this value into the equation, getting 5 = 8x + 8.
- Solve the equation for x, which represents the time.
- Subtract 8 from both sides to isolate 8x, which yields -3 = 8x.
- Divide by 8 to solve for x, giving x = -3/8.
This result doesn't make practical sense because time cannot be negative, so it's likely that the equation doesn't apply or that there was a mistake in the interpretation or formulation of the problem.