Question

Adnan is training for a race and tracks the lengths of his runs leading every week. His list for the first month is as follows: {1,2.5,4,5.5}

Which equation represents the growth of the lengths of his runs? Select one:
a.y=x+1.5
b.y=1.5x-.5
c.y=5.5x-1.5
d.y=5.5-x

Answer 1

The equation that represents the growth of the lengths of Adnan's runs is b. y = 1.5x - 0.5. This is confirmed by the consistent increase of 1.5 in the lengths of Adnan's runs each week, which matches the slope in the equation.

Step-by-step explanation:

To determine which equation represents the growth of the lengths of Adnan's runs, we need to look at the pattern in the data {1, 2.5, 4, 5.5}. To find the correct equation, we can calculate the difference between each pair of successive lengths: 2.5 - 1 = 1.5, 4 - 2.5 = 1.5, and 5.5 - 4 = 1.5. This constant difference suggests that the lengths are increasing by 1.5 each time, indicating a linear relationship. Therefore, the coefficient of x (the slope) should be 1.5. Now, let's check the starting value. When x = 1 (the first week), y = the length of the run, which is also 1. Plugging these values into each option, we are looking for an equation that gives y = 1 when x = 1. Only option b does this: y = 1.5(1) - 0.5 = 1. Additional confirmation comes from the fact that this equation will also produce the subsequent run lengths correctly. If x = 2, y = 1.5(2) - 0.5 = 2.5; if x = 3, y = 1.5(3) -0.5 = 4; and if x = 4, y = 1.5(4) - 0.5 = 5.5.