which of these graphs shows a proportional relationship?

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship is a linear relationship (straight line) that passes through the origin ((0,0)). The equation is (y = kx), where (k) is the constant of proportionality. So, we need to check which graph has a straight line passing through ((0,0)).

Step2: Analyze Each Graph

• Top - Left Graph: The line starts at ((0,5)) (y - intercept is 5), so it does not pass through the origin. Not proportional.
• Top - Right Graph: The line starts at ((0,1)) (y - intercept is 1), so it does not pass through the origin. Not proportional.
• Bottom - Left Graph: The line is horizontal (constant (y = 2)), which is not a proportional relationship (since it's not of the form (y=kx) with (k) non - zero and it doesn't pass through the origin).
• Bottom - Right Graph: The line passes through the origin ((0,0)) and is a straight line, so it represents a proportional relationship.

Answer:

The graph at the Bottom - Right (the fourth graph) shows a proportional relationship.