Question

Miguel has started running. He runs 1 mile the first week. His goal is to run 2 miles farther than his distance for the previous week. Which linear formula represents this scenario?

A) y = 2x + 1
B) y = 1x + 2
C) y = -1x + 2
D) y = 2x - 1

Answer 1

To represent Miguel's running progress with a formula, we look for a linear equation that starts with 1 mile and increases by 2 miles each week. The correct linear formula that fits this scenario is y = 2x + 1.

Step-by-step explanation:

The student is asking about the linear formula that best represents the scenario of Miguel's running routine, where he runs 1 mile the first week and plans to run 2 miles farther each subsequent week. To express Miguel's distance run in any given week, we use the linear formula y = mx + b, where y represents the total distance run, m is the constant rate of increase per week, x is the number of weeks, and b is the initial value or starting point.

Since Miguel starts at 1 mile and adds 2 miles each week, the correct formula would be the one that starts at 1 and increases by 2 for each value of x. Thus the correct answer is y = 2x + 1, which represents a starting point of 1 mile plus an additional 2 miles for each week that passes.