Question

"Lionel loves soccer, but has trouble motivating himself to practice. So, he

incentivizes himself through video games. There is a proportional relationship
between the amount of drills Lionel completes, in x, and for how many hours
he plays video games, in y. When Lionel completes 10 drills, he plays video
games for 30 minutes. Write the equation for the relationship between x and y."

A) y = 0.05x
B) y = 10x
C) y = 0.5x
D) y = 5x

Answer 1

The equation for the relationship between the number of drills completed and the number of hours Lionel plays video games is y = 0.05x.

Step-by-step explanation:

The given problem states that there is a proportional relationship between the number of drills completed (x) and the number of hours Lionel plays video games (y). We can express this relationship using the slope-intercept form of a linear equation, which is y = mx + b. Here, m represents the slope and b represents the y-intercept.

Since the relationship is proportional, the slope is constant. We can find the slope by dividing the change in y by the change in x. According to the problem, when Lionel completes 10 drills, he plays video games for 30 minutes (0.5 hours). Therefore, the slope is 0.5/10 = 0.05.

Now we can write the equation: y = 0.05x + b. To find the value of b, we need to substitute the values of x and y from one of the given coordinate points. Choosing the point (10, 0.5), we can substitute x = 10 and y = 0.5 into the equation to solve for b: 0.5 = 0.05(10) + b. Simplifying the equation, we get b = 0.5 - 0.5 = 0.

Therefore, the equation for the relationship between x and y is y = 0.05x.