Question

mathematics 7 - 7 - full year
topic 2 assessment
part a
what is the constant of proportionality, and what does it mean in this situation?
use the drop - down menus to show and explain your answer.
the graph shows how many bottles a machine caps in a certain number of seconds.
part a
what is the constant of proportionality, and what does it mean in this situation?
use the drop - down menus to show and explain your answer
the constant of proportionality is choose... the machine caps choose... bottles in choose...
part b

Explanation:

Step1: Find the constant of proportionality

The constant of proportionality \( k \) for a proportional relationship \( y = kx \) (where \( y \) is the number of bottles capped and \( x \) is the number of seconds) can be found using the formula \( k=\frac{y}{x} \).
Take a point on the graph, say \( (15,300) \). Then \( k = \frac{300}{15}=20 \).

Step2: Interpret the constant of proportionality

In the context of the problem, \( y \) is the number of bottles capped and \( x \) is the number of seconds. The formula \( y = kx \) means that the number of bottles capped (\( y \)) is related to the number of seconds (\( x \)) by the multiplier \( k \).

Answer:

The constant of proportionality is \( 20 \); the machine caps \( 20 \) bottles in \( 1 \) second.