A machine is filling a container with candy. The graph below shows the relationship between the amount of candy C (in grams) in the container and the time T (in seconds) since the machine began filling the container.

Question

Amount of candy (grams)
C200400600800100012001400160018002000T1234567890
Time (seconds)mmk

(a)Write an equation to represent the relationship between C and T.


(b)Choose the correct statement to represent this relationship.

The machine is filling the container with 200 grams of candy per second.
The machine is filling the container with 1 gram of candy per 200 seconds.
The machine is filling the container with 400 grams of candy per second.
The machine is filling the container with 1 gram of candy per 400 seconds.

Answer 1

(a) To find the equation that represents the relationship between C and T, we first need to determine the slope of the graph.

From the graph, we can see that for every 2 seconds (T), the candy in the container increases by 200 grams (C). Therefore, the slope is 200 grams per 2 seconds, which can be simplified to 100 grams per second.

Using the slope-intercept form of a linear equation, we can write the equation:

C = 100T

(b) The correct statement to represent this relationship is:

The machine is filling the container with 100 grams of candy per second.