Question

question 6 of 10 (1 point) | question attempt: 1 of unlimited

(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 400 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 200 seconds.

Explanation:

Step1: Determine the slope of the line

Since the line passes through the origin \((0,0)\), and assuming from the graph (if we consider a point like \((1,400)\) - as the rate of change of amount of candy with respect to time). The slope \(m\) of a line \(C = mT\) (where \(C\) is the amount of candy in grams and \(T\) is the time in seconds) is given by \(m=\frac{\Delta C}{\Delta T}\). If for \(T = 1\) second, \(C=400\) grams, then the equation of the line (using the direct - variation form \(y = kx\), here \(C = mT\)) is \(C = 400T\).

Step2: Interpret the slope as a rate

The slope \(m = 400\) in the equation \(C = 400T\) has the units \(\frac{\text{grams}}{\text{second}}\). In the context of the problem, where \(C\) is the amount of candy (in grams) and \(T\) is the time (in seconds), the slope represents the rate at which the machine is filling the container. The formula for the rate \(r=\frac{C}{T}\). Substituting \(C = 400T\) into the rate formula, we get \(r=\frac{400T}{T}=400\) grams per second.

Answer:

(a) \(C = 400T\)
(b) The machine is filling the container with 400 grams of candy per second.