Question

The table below represents the displacement of a horse from its barn as a function of time:

Answer 1

A. The y-intercept (b) of a linear equation is obtained when x = 0. Therefore from the given table,

y - intercept = 8

Since at time zero the displacement is 8 ft, this means that the horse was already outside the barn initially.

B. The average rate of change of the function represents the slope of the linear equation (m). This can be calculated using the formula:

average rate of change = m = (y2 – y1) / (x2 – x1)

m = (158 – 58) / (3 – 1)

m = 50

C.  Since we have determine the y-intercept and the slope, we can formulate the linear equation:

y = m x + b

y = 50 x + 8

The domain is the value of x. When y = 508, x is equivalent to

508 = 50 x + 8

x = 10 hrs