Question

Graphs of Proportional Relationships Quick Check
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Question
Use the image to answer the question.

A figure shows four graphs labeled A, B, C, and D, each with an x and y axis and 0 at the origin, and each showing a curve. Graph A shows a straight line with a negative slope having x and y intercepts. Graph B shows a straight line with a positive slope having a y intercept above origin. Graph C shows an increasing concave up curve initiating at the origin. Graph D shows a straight line with a unit slope.

Decide which graph shows a proportional relationship.

(1 point)
Responses

D
D

C
C

A
A

B
B
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Answer 1

In a proportional relationship, for any two quantities, one quantity is a constant multiple of the other. This is often expressed as y = kx, where k is a constant, y is the dependent variable, and x is the independent variable. In a graph, proportional relationships are represented as straight lines passing through the origin (0,0), with the slope (rise over run) of the line being the constant (k).

From the descriptions provided for each graph:

Graph A: Shows a straight line with a negative slope with x and y intercepts. Though it has x and y intercepts, if it also passes through the origin, it could potentially represent a proportional relationship, just with a negative constant. However, the statement doesn't clarify that it passes through the origin, so we can't conclude this with certainty.

Graph B: Shows a straight line with a positive slope having a y intercept above the origin. Since it does not go through the origin (because of the positive y-intercept), this line does not represent a proportional relationship.

Graph C: Shows an increasing concave up curve initiating at the origin. Even though it begins at the origin, the fact that it's a curve (not a straight line) indicates that this is not a proportional relationship.

Graph D: Shows a straight line with a unit slope (which means the slope is 1). Since it's a straight line, and nothing in the description contradicts that it goes through the origin, this graph could be depicting a proportional relationship where the constant k equals 1.

Based on the information provided and the definitions:

The correct response is:

D

Graph D shows a proportional relationship.