Question

topic 2 linear relationships

1. trung and her band are recording a cd. after reading an article about great songs, they determine that each song they record should be about 3.1 minutes. the band then decides to add a special behind the lyrics feature that is 3.7 minutes long.

a. write an equation that represents the total length of the cd in minutes, y, given x number of songs recorded.
b. graph the equation.
c. identify the slope and y - intercept of the graph. explain what each means in terms of the situation.
trung and her band decide to put 12 songs on the cd, plus the behind the lyrics feature. how many minutes long will the cd be?

Explanation:

Step1: Write the linear equation

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the \(y -\)intercept (initial value).
Each song is \(3.1\) minutes long (so the rate of change for the length of the CD with respect to the number of songs is \(3.1\)), and the behind - the - lyrics feature is \(3.7\) minutes (the initial value when \(x = 0\)).
The equation is \(y=3.1x + 3.7\).

Step2: Find the length of the CD when \(x = 12\)

Substitute \(x = 12\) into the equation \(y=3.1x + 3.7\).

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Answer:

The CD will be \(40.9\) minutes long.