Linear Equations of Problem Scenarios

Question

The file size of a video depends on the playing time of the video. The table shows the playing time in minutes,x, and file sizes of these videos, y, in megabytes,MB. Write an equation that represents the problem situation.

the chart has “Playing time, x (min)” on the top on the left with the numbers 0.5, 1.5, 2, 4.5, and 5 listed. On the right the chart has “File size, y (MB)” at the top and the numbers 60,180,240,540 and 600 listed. What is the equation?

Answer 1

Hello, Elizabeth,

The table:

This looks like it might be a straight line, so I'll check by calculating the slope at various points. The slope is the Rise/Run, so the slope between the first two points is (180-60)/(1.5-0.5) = 120. The slope between the 2nd and last points is (600-180)/(5-1.5) = 120. In fact, the slope is 120 regardless of which points I choose.

This means we have a linear equation with slope 120. That can be expressed as:

y = 120x + b

We need the b, which is just the value of y when x = 0. It looks like zero, but we can confirm b by inputting any of the data pairs we've been given.

For (2, 240):

240 = 120*(2) + b

240 = 240 + b

b = 0

So the equation is simply: y = 120x. Y is in units of MB and X is in units of minutes. The slope of 120 represents MB/min.

The equation does not tell us which movies to watch, however. If you can develop one for that, Netflix will pay well, if it is better than the one they've developed.

Bob