Question

20 POINTS

Janet is training for a marathon. She decides to track her time per mile, in minutes, for 8 weeks. Which equation best fits the data?

A graph is labeled as Marathon Training. The horizontal axis is labeled as Weeks and the vertical axis is labeled as Time per mile left parenthesis minutes right parenthesis. The values on the horizontal axis range from 0 to 10 in increments of 2 and the values on the vertical axis range from 0 to 10 in increments of 2. Nine points are marked on the graph with their coordinates approximately equal to (0, 10), (1, 9 decimal point 9), (2, 9 decimal point 6), (3, 9 decimal point 5), (4, 9 decimal point 4), (5, 9 decimal point 2), (6, 9), (7, 8 decimal point 7), and (8, 8 decimal point 6).
A.y=0.18x + 10.06
B.y=−0.18x + 10.06
C.y = 2x + 8.6
D.y = −2x + 8.6

Answer 1

B. y=−0.18x + 10.06

Explanation:

Let us compute the average of the slope between points

(9.9-10)/(1-0) = -0.1

(9.6-9.9)/(2-1) = -0.3

(9.5-9.6)(3-2) = -0.1

(9.4-9.5)/(4-3) = -0.1

(9.2-9.4)/(5-4) = -0.2

(9 - 9.2)/(6-5) = -0.2

(8.7-9)/(7-6) = -0.3

average is (0.1+0.3+0.1+0.1+0.2+0.2+0.3)/7 = -0.186

The y- intercept we know from point (0,10) is ten

Thus, from the choices given, the equation that best first the data is

y=−0.18x + 10.06.