Question

Distance (in miles) 14.2 28.5 42.6 57.4 71.6 85.7 100.2 114.8 Time in hours 25 .5 .75 (a) Without graphing, determine if the data shown in the table is approximately linear. If it is, compute spent driving.tTraveled, D and interpret the slope of the approximating line. 1.25 1.5 1.75 2 (b) The marginal change, given by the slope, is the change in the y-value (distance traveled) as the value of x (time in hours spent driving) increases by one unit. If the time spent driving increased from 2 hours to 3 hours, what distance would your marginal change predict as the distance traveled? (c) Notice: If your time spent driving is 0 hours, the distance you've traveled, D, is also zero miles. Use this y-intercept information to write the equation of your approximating line: D = a + bt where hours driven, D-miles traveled

Answer 1

a) To check if the data is linear without graphing, we will check if the slope remains constant throughout the data set

slope = change in distance/change in time

we see that the change in time is constant in the data set = 0.25 hrs

Hence we find the different values of change in distance = 14.3, 14.1 , 14.8, 14.2, 14.1, 14.5 , 14.6

Since the values of change in distance are almost constant too, we can say the graph is linear.

The slope of the graph is = 14.37/0.25 = 57.48

b) Since the slope is constant we can say

Change in distance/change in time = 57.48

x-114.8 / (3-2) = 57.48 ...... x is the distance traveled in 3 hours

x = 57.48 + 114.8 = 172.28 mi

c) Our equation is

D = a + bt , a would be the intercept of the graph on the t axis, while b is the slope

we already have calculated the slope to be 57.48 mi/hr

Hence we have

D = a + 57.48*t

Also we know at t = 0 D =0

0 = a + 57.48*0

a = 0

Our equation is

D = 57.48*t

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