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
A
The correct answer is A. Graph A shows a straight line with a negative slope that passes through the origin. This indicates a proportional relationship where the y-values decrease at a constant rate as the x-values increase.
sure??
To determine which graph shows a proportional relationship, we need to understand what a proportional relationship means. In a proportional relationship, as the x-values increase or decrease, the y-values also increase or decrease in a consistent ratio.
Looking at the graphs described:
- Graph A shows a straight line with a negative slope. It intersects both the x and y-axes, suggesting non-proportional behavior.
- Graph B shows a straight line with a positive slope. It has a y-intercept above the origin, also indicating non-proportional behavior.
- Graph C shows an increasing concave up curve that originates from the origin. This curve shape suggests a non-linear relationship, so it is not proportional.
- Graph D shows a straight line with a unit slope. A unit slope means that for every increase of 1 unit in the x-values, there is a corresponding increase of 1 unit in the y-values. This consistent ratio indicates a proportional relationship.
Therefore, the graph that shows a proportional relationship is graph D.