Question

2. A group of workers are harvesting oranges at a constant rate. An equation that represents the number of oranges the workers picked over a period of time, in hours, is y = 9x + 15. Complete sentences. Handwritten. Show work.

(a) What is the slope and the y-intercept for the equation that represents the number of oranges the workers picked over a period of time?
(b) What is the rate of change (slope) and the initial amount (y-intercept)? Explain the meaning of the rate of change and the initial amount for the situation. Answer in complete sentences

Answer 1

The equation for the number of baskets is an illustration of a linear function.

• The slope is 9, and the y-intercept is 15
• The rate of change is 9, and the initial amount is 15

The function is given as:

`\bold{y=9x+15}`

(a) The slope and the y-intercept

A linear function is represented as:

`\bold{y=mx+b}`

Where:

m represents the slope, and b represents the y-intercept

By comparison, the slope is 9, and the y-intercept is 15

(b) The rate of change and the initial amount

The rate of change is the slope, and the initial amount is the y-intercept

By comparison, the rate of change is 9, and the is 15

Answer 2

Explanation:

(a) The slope of the equation y = 9x + 15 is 9, and the y-intercept is 15.

(b) The rate of change or slope of the equation y = 9x + 15 is 9, which represents the constant rate at which the workers are picking oranges. For every hour of work, they pick 9 more oranges. The initial amount or y-intercept of 15 represents the number of oranges they would have picked if they had started working from the beginning of time. However, since this is not possible, it can be interpreted as the number of oranges they picked before starting to work for the period of time that is being measured.