which linear graph represents a proportional relationship?
which linear graph represents a proportional relationship?
Answer
Explanation:
Step1: Recall proportional relationship rule
A proportional relationship (direct variation) is a linear relationship of the form ( y = kx ), where ( k ) is the constant of proportionality. The graph of such a relationship must pass through the origin ((0,0)) because when ( x = 0 ), ( y = 0 ).
Step2: Analyze the first graph
The first graph has a ( y )-intercept at ( (0,1) ), so it does not pass through the origin. Its equation is of the form ( y = mx + b ) with ( b \neq 0 ), so it is not a proportional relationship.
Step3: Analyze the second graph
The second graph passes through the origin ((0,0)), which fits the form ( y = kx ) (since when ( x = 0 ), ( y = 0 )). So this graph represents a proportional relationship.
Answer:
The linear graph that represents a proportional relationship is the second graph (the one with the blue dot selected, passing through the origin ((0,0))).