Question

aiden and some of his friends compared the amount of time they studied for a math quiz and the scores they got. then, aiden estimated a line of best fit.
quiz scores
study time in minutes (x) 40 50 20 70 10 20 30
points (y) 8 9 7 10 5 6 7
the equation for the line of best fit is $y = 0.08x + 4.7$.
what prediction could you make based on the value of the $y$-intercept?
studying 10 more minutes should increase your score around 1 point.
without studying, you would score around 4 or 5 points.
it is impossible to score below 4.7 on this quiz.
studying 1 more minute would do little to increase your score.

Explanation:

Step1: Identify y-intercept meaning

The y-intercept is the value of $y$ when $x=0$. Here, $x$ is study time (minutes), so $x=0$ means no study time.

Step2: Calculate y at x=0

Using $y = 0.08x + 4.7$, substitute $x=0$: $y = 0.08(0) + 4.7 = 4.7$.

Step3: Match to option

4.7 is approximately 4 or 5, so the prediction is about scoring around 4 or 5 with no study time.

Answer:

Without studying, you would score around 4 or 5 points.