The table shows the distance, in miles, that an athlete will run each week for
6
weeks to prepare for a half marathon.
Distance to Run Each Week
Week Distance (miles)
1
13
2
15.5
3
15.5
4
22.5
5
23
6
30
The equation
y
=
3.25
x
+
8.5
models the distance,
y
,
in miles, that the athlete will run in week
x
.
For which weeks is the number of miles given by the equation greater than the actual number of miles the athlete will run?
Select all that apply.
A.
week
1
B.
week
2
C.
week
3
D.
week
4
E.
week
5
F.
week
6
To determine when the number of miles given by the equation is greater than the actual number of miles the athlete will run, we need to compare the values from the equation to the corresponding values in the table.
For week 1, the equation gives:
y = 3.25(1) + 8.5 = 3.25 + 8.5 = 11.75
The actual number of miles for week 1 is 13.
11.75 < 13, so the equation is not greater than the actual number of miles for week 1.
For week 2, the equation gives:
y = 3.25(2) + 8.5 = 6.5 + 8.5 = 15
The actual number of miles for week 2 is 15.5.
15 < 15.5, so the equation is not greater than the actual number of miles for week 2.
For week 3, the equation gives:
y = 3.25(3) + 8.5 = 9.75 + 8.5 = 18.25
The actual number of miles for week 3 is 15.5.
18.25 > 15.5, so the equation is greater than the actual number of miles for week 3.
For week 4, the equation gives:
y = 3.25(4) + 8.5 = 13 + 8.5 = 21.5
The actual number of miles for week 4 is 22.5.
21.5 < 22.5, so the equation is not greater than the actual number of miles for week 4.
For week 5, the equation gives:
y = 3.25(5) + 8.5 = 16.25 + 8.5 = 24.75
The actual number of miles for week 5 is 23.
24.75 > 23, so the equation is greater than the actual number of miles for week 5.
For week 6, the equation gives:
y = 3.25(6) + 8.5 = 19.50 + 8.5 = 28
The actual number of miles for week 6 is 30.
28 < 30, so the equation is not greater than the actual number of miles for week 6.
Based on this analysis, the equation is greater than the actual number of miles for weeks 3 and 5.