Question

question
as a math teacher, florence frequently makes photocopies of fun activities for her students to do. when the copies come out of the copy machine, they form a stack.
this table shows the relationship between the number of copies in the stack, x, and the height (in millimeters) of the stack, y.

x (copies)	y (millimeters)
50	2
75	3
100	4

according to the values in the table, do x and y have a proportional relationship?
yes
no
correct answer
yes
y = 0.04x

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship between two variables \( x \) and \( y \) means \( y = kx \), where \( k \) is the constant of proportionality. This implies \( \frac{y}{x} \) should be constant for all pairs of \( x \) and \( y \).

Step2: Calculate \( \frac{y}{x} \) for Each Pair

• For \( x = 25 \), \( y = 1 \): \( \frac{y}{x} = \frac{1}{25} = 0.04 \)
• For \( x = 50 \), \( y = 2 \): \( \frac{y}{x} = \frac{2}{50} = 0.04 \)
• For \( x = 75 \), \( y = 3 \): \( \frac{y}{x} = \frac{3}{75} = 0.04 \)
• For \( x = 100 \), \( y = 4 \): \( \frac{y}{x} = \frac{4}{100} = 0.04 \)

Step3: Check Consistency

Since the ratio \( \frac{y}{x} \) is \( 0.04 \) for all given pairs, the relationship is proportional (as \( y = 0.04x \), which fits \( y = kx \) with \( k = 0.04 \)).

Answer:

yes