A bike is travelling at a constant speed. After 35 minutes, it travels 7 miles. Which table represents the relationship between the time in minutes, x, and the distance the bike travles, y?

Table 3

x | y

50 | 10

60 | 12

70 | 14

80 | 16

Step-by-step explanation:

x = time in minutes

y = distance travelled

Given that the bike travelled 7 miles after 35 minutes at a constant speed, the rate of change = .

Thus, the table that represents the relationship between the time in minutes, x, and the distance the bike travles, y would have the same rate of change of ⅕.

Calculate the rate of change of each table using any two given pairs on the table:

Table 1: using (50, 10) and (55, 12)

Rate of change =

Table 2: using (60, 10) and (72, 12)

Rate of change =

Table 3: using (50, 10) and (60, 12)

Rate of change =

This table has the same rate of change.

Table 4: using (70, 10) and (84, 12)

Rate of change =

Table 3 represents the relationship between the time in minutes, x, and the distance the bike travles, y.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.