Question

A group of workers are picking apples at a constant rate. An equation that represents the number of baskets of apples the workers picked over a period of time, in hours, is y = 2x + 8.

(a) What are the slope and the y-intercept for the equation that represents the number of baskets of apples the workers picked over a period of time?
(b) What are the rate of change and the initial amount? Explain the meaning of the rate of change and the initial amount for the situation.
(c) Use graph paper to draw a graph representing the situation. Label the axes appropriately.

Answer 1

(a) Slope and intercept

In the equation y = 2x +8, the coefficient of x is the slope and the constant is the y-intercept.

Thus,

slope = 2; y-intercept = 8

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(b) Rate of change and initial amount

The rate of change is the slope. The units of y are baskets of apples and the units of x are hours. So,

rate of change = 2 baskets of apples per hour

The initial amount when x = o.

When x = 0, y = 8. so

Initial amount = 8 baskets of apples

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(c) Graph

Your graph should look something like the one below.