Question

the equation of the line is \\(y \approx -1.02x + 7.09\\). using the line, she predicted that when the value of \\(x\\) is \\(0.5\\), the value of \\(y\\) will be approximately \\(7.6\\). what was her mistake?

she drew the line of best fit incorrectly.
she used the line of best fit to predict \\(y\\) for an incorrect value of \\(x\\).
she forgot the minus sign before the first term on the right side of the equation when she predicted \\(y\\).
she plugged \\(0.5\\) into the equation for \\(y\\) instead of \\(x\\) and actually predicted \\(x\\) instead of \\(y\\).

Explanation:

Analyze the prediction equation

Using the Line of Best Fit knowledge point
The given equation of the line of best fit is:

$$y \approx -1.02x + 7.09$$

Calculate the correct prediction for x = 0.5

Using the Line of Best Fit knowledge point
Substitute \(x = 0.5\) into the equation:

$$
LATEXBLOCK0
$$

Evaluate the student's calculation error

Using the Line of Best Fit knowledge point
The student predicted \(y \approx 7.6\). Let us test if she omitted the negative sign:

$$
LATEXBLOCK1
$$

This matches her prediction of \(7.6\).

Identify the correct multiple-choice option

The calculation shows that she forgot the negative sign in front of the first term (\(-1.02x\)) when evaluating the expression. This corresponds to the third option.

Answer:

• She drew the line of best fit incorrectly.
• She used the line of best fit to predict y for an incorrect value of x.
• She forgot the minus sign before the first term on the right side of the equation when she predicted y. (Correct answer)
• She plugged 0.5 into the equation for y instead of x and actually predicted x instead of y.