Question

Hilary makes $8 per hour raking lawns in her neighborhood. Which graph models her total earnings y from x hours of raking?

a. A linear graph

b. A parabolic graph

c. An exponential graph

d. A constant graph

Answer 1

The graph that models Hilary's total earnings from raking lawns for a given number of hours is a linear graph, with the earnings increasing by $8 for each additional hour of work.

Step-by-step explanation:

The student asked which graph models Hilary's total earnings y from raking lawns for x hours at a rate of $8 per hour. The correct answer is a linear graph.

Since Hilary earns a fixed amount per hour, this relationship is directly proportional: as the number of hours increases, her earnings increase at a constant rate. Graphically, this is represented as a straight line with a slope equal to the hourly rate, which in this case is $8. Therefore, for every additional hour worked, Hilary earns an additional $8. The equation representing her total earnings would then be y = 8x.

To put it in context, similar to the example given where Svetlana's total earnings from tutoring can be expressed as y = 25 + 15x, and the auto mechanic's charges are y = 55x + 75, Hilary's earnings are simply y = 8x because there is no one-time fee in her case.