Question

the equation for the line of best fit is $y = \frac{1}{2}x + 62$.\
which statements are supported by this equation? select all that apply.\
a school with a student population of 1,100 should have about 612 student athletes.\
when the student population increases by 50, the number of student athletes increases by roughly 100.\
in general, there will be about 1 student athlete for every 62 students.\
a school with 287 student athletes should have a student population of about 450.

Explanation:

Step1: Assume x is student population, y is athletes

Equation: $y = \frac{1}{2}x + 62$

Step2: Check first statement (x=1100)

$y = \frac{1}{2}(1100) + 62 = 550 + 62 = 612$ → Correct

Step3: Check second statement (Δx=50)

Δy = $\frac{1}{2}(50) = 25 ≠ 100$ → Incorrect

Step4: Check third statement (ratio)

Ratio: $\frac{y}{x} ≈ \frac{1}{2}$ (not 1/62) → Incorrect

Step5: Check fourth statement (y=287)

$287 = \frac{1}{2}x + 62$ → $\frac{1}{2}x = 225$ → $x=450$? Wait: $287-62=225$, $x=450$. But wait: Is this supported? Wait, the line of best fit predicts y from x, not x from y directly (though mathematically solvable, but the question is about support. However, the first statement is definitely correct as it uses x→y prediction. The fourth: Let's recalculate: $y=287$, $x=2*(287-62)=450$. But does the equation support predicting x from y? Typically, regression predicts dependent variable from independent. Assuming x is independent (population), predicting x from y is not standard. So only first statement is supported.

Wait correction: The fourth statement says "a school with 287 athletes should have population ~450". Mathematically, solving for x gives 450, but is this a valid use of the line of best fit? If the line is y (athletes) vs x (population), then predicting x from y is extrapolating in reverse, which is not always supported. The first statement is a direct prediction of y from x, which is valid. So only the first statement is correct.

Final Answer: A school with a student population of 1,100 should have about 612 student athletes.

Answer:

A school with a student population of 1,100 should have about 612 student athletes.