Question

Difficulty: EasyInterpreting Linear Relationships in Context

A worker at a distribution center packages boxes at a constant rate. The total number of boxes, $B$ , the worker has packaged $h$ hours after starting their shift can be modeled by the equation $B = 12h + 15$ . According to the model, how many boxes were already packaged at the start of the worker's shift?

Answer: 15 boxes

Answer

At the start of the worker's shift,

15

boxes were already packaged.

In the linear model

B = 12h + 15

, the term

15

is the constant term (y-intercept), which represents the value of

B

when

h = 0

. In this context,

h = 0

represents the start of the worker's shift. Therefore,

15

boxes were already packaged at the start of the shift.

Step-by-Step Solution

1

Identify the value of

h

that represents the start of the shift.

h = 0

The variable

h

represents the number of hours since the shift started, so the start of the shift corresponds to

0

hours.

2

Substitute

h = 0

into the given equation to find the value of

B

.

B = 15

Evaluating the equation at

h = 0

gives the initial number of packaged boxes, which is represented by the constant term of the linear equation.

Key Concept

Interpreting the y-intercept of a linear relationship in context

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Topics

Interpreting Linear Relationships in Context

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