Question

Two relationships between x and y are shown below. Relationship 1 is represented by the blue, solid graph. Relationship 2 is represented by the red, dashed graph.

a) Identify the relationship with a steeper slope.
b) Identify the relationship with a shallower slope.
c) Determine the x-value where the two relationships intersect.
d) Find the y-value at x = k/2 for Relationship 1.

Answer 1

a) Relationship 2 has a steeper slope.

b) Relationship 1 has a shallower slope.

c) The x-value where the two relationships intersect is x = k/4.

d) The y-value at x = k/2 for Relationship 1 is y = k/4.

Step-by-step explanation:

a) To determine which relationship has a steeper slope, we compare the steepness of their graphs. A steeper slope means a greater rate of change. In this case, the red, dashed graph of Relationship 2 exhibits a steeper incline than the blue, solid graph of Relationship 1.

b) Conversely, a shallower slope indicates a slower rate of change. The blue, solid graph of Relationship 1 has a gentler incline compared to the red, dashed graph of Relationship 2, making Relationship 1 the one with a shallower slope.

c) The x-value of intersection can be found by identifying the point where the two graphs cross. In this case, the intersection occurs at x = k/4. At this point, the values of x are equal for both relationships.

d) To find the y-value at x = k/2 for Relationship 1, we substitute x = k/2 into the equation for Relationship 1. The resulting y-value is y = (k/2)/2, simplifying to y = k/4. Therefore, at x = k/2, the y-value for Relationship 1 is k/4.