Question

Tanica drew a line of best fit on a scatterplot, as shown below. On a graph, a trend line has a negative slope. The equation of the line is y = -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?

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

Answer 1

Based on this analysis, the mistake made by Tanica can be identified as:

3) She forgot the minus sign before the first term on the right side of the equation when she predicted y.

How to identify Tanica mistake

The mistake made by Tanica can be determined by analyzing the given information.

The equation of the line of best fit is y = -1.02x + 7.09. This means that the slope of the line is -1.02, indicating a negative slope.

Therefore, as x increases, y is expected to decrease.

According to Tanica's prediction, when x is 0.5, the value of y will be approximately 7.6.

Let's plug 0.5 into the equation

y = -1.02(0.5) + 7.09

y = -0.51 + 7.09

y ≈ 6.58

However, when we plug in x = 0.5 into the equation, the value is 6.58 not 7.6

However, by ignoring the negative sign, the value becomes 7.6

Therefore;

Based on this analysis, the mistake made by Tanica can be identified as:

3) She forgot the minus sign before the first term on the right side of the equation when she predicted y.