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
A
A
C
C
B
B
D
B
To determine which graph shows a proportional relationship, we need to understand what a proportional relationship means. In a proportional relationship, the ratio between the dependent and independent variables remains constant.
Looking at the graphs:
- Graph A shows a straight line with a negative slope and x and y intercepts. It does not indicate a proportional relationship because the slope is negative.
- Graph B shows a straight line with a positive slope and a y-intercept above the origin. It does not represent a proportional relationship because the line is not passing through the origin.
- Graph C shows an increasing concave up curve initiating at the origin. It does not indicate a proportional relationship because the curve is not a straight line.
- Graph D shows a straight line with a unit slope, meaning the line has a constant slope of 1. This indicates a proportional relationship because the ratio between the dependent and independent variables is constant.
Therefore, the correct answer is D: Graph D represents a proportional relationship.