Question

Question 2a)Tell is this relationship is a direct variation.The equations -15x + 4y = 0 relates the length of a videotape in inches x to its approximate playing time in seconds y.Please enter yes, or nob)Question 3Using the previous function from question 2 , could you please find the playing time of a videotape 1 foot long? seconds

Answer 1

If two variables x and y are proportional (direct variation), one can be written in terms of the another using a constant of proportionality, which is often represented using a letter k:

`y=kx`

Isolate y from the given relationship:

`\begin{gathered} -15x+4y=0 \\ \Rightarrow4y=15x \\ \Rightarrow y=(15)/(4)x \end{gathered}`

As we can see, the variable y can be written in terms of x through a constant of proportionality equal to 15/4. Then, the relationship is a direct variation. The answer to Question 2 is: yes.

To find the playing time, replace the value of x. Since 1 foot is equal to 12 inches and the equation y=15/4 x works when x is in inches and y is in seconds, replace x=12 to find the playing time in seconds:

`\begin{gathered} y=(15)/(4)*12 \\ =45 \end{gathered}`

Then, the playing time for a tape 1 foot long is 45 seconds. The answer to Question 3 is: 45.