Question

The table shows the amounts of storage left y (in gigabytes) on a music playing device when there are x songs on the device.

A. Write an equation that models the amount of storage left as a function of the number of songs.

B. Interpret the slope and y-intercept of the line of fit.​

Answer 1

(a) The equation that models the given function is y = -0.004x + 16.

(bi) The slope shows that as the number of songs on the device increases, the amount of storage left decreases.

(bii) The y intercept shows that initially when there is zero song in the device, the amount of storage left is maximum.

How to write the equation that models the function?

The equation that models the given function is determined as follows;

y = mx + c

where;

• m is the slope of the line
• c is the y - intercept of the line

The slope of the line is calculated as follows;

using the points (0, 16) and (825, 12.7)

m = Δ y / Δ x

m = ( 12.7 - 16) / ( 825 - 0)

m = -0.004

The y - intercept of the line occurs at point x = 0

c = 16

The equation of the line becomes;

y = -0.004x + 16