A.) Hobbs:
We know that the dependent variable goes on the y axis and that the independent variable goes on the x axis. In this case, the cost changes according to the number of hours, so x = hours and y = cost. SInce it states that both of the relationships are linear, this means that we should look for a slope equation: y = (slope) * x + (y intercept).
We begin with y2 - y1/x2 - x1. In this case, the x value changes by a value of 0.5 and the y value changes by 17, making our slope 17/0.5, or 34.
Now that we know the m value, write down the equation y = 34x + b, and plug in the values you already know. For instance, if we use the first pair:
25 = 34 * 0.5 + b
25 = 17 + b, which means b = 8. Your equation for this is y = 34x + 8.
McGee:
Using the same method, 144 - 80/4 - 2 = 64/2 = 32.
y = 32x + b
80 = 32 * 2 + b, so b = 16.
Now let's plug in the x values.
Hobbs: y = 34(3) + 8, so y = $110
McGee: y = 32(3) + 16 = $112
Therefore, the customers should go to Hobbs for 3 hour mule rides, since it's less expensive.
B.) Yes. this would affect the answer to part A. Since the x value has changed, the y value would also have to change for the equation to be true. FOr instance:
34(5) + 8 = $178
32(5) + 16 = $176
