Question

1. which scatter plot most likely has a line of best fit represented by y = 3x + 1? (options a, b, c, d with scatter plots)
2. students in grades 1 through 9 were given a survey in which they were asked what they want to be when they grow up. they were then given 20 choices and were asked to select all options that interested them. the scatterplot shows their responses.

a) estimate the equation of the line of best fit.
b) use the equation to predict how many choices a 4th grader would make. (scatter plot with grade level and number of jobs axes)

Explanation:

Step1: Analyze line properties

The line \(y = 3x + 1\) has a positive slope (3) and y-intercept 1, so points should show a strong positive trend.

Step2: Check scatter plots

Plot C has points clustered along a steep positive line, matching the slope and intercept characteristics.

Step1: Estimate line of best fit

The scatter plot shows a negative linear trend. Pick two points: (0,18) and (10,3). Slope \(m = \frac{3-18}{10-0} = -1.5\). Y-intercept \(b = 18\). Equation: \(y = -1.5x + 18\).

Step2: Predict for 4th grader

Substitute \(x = 4\) into the equation: \(y = -1.5(4) + 18 = -6 + 18 = 12\).

Answer:

C

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