Relationship B has a greater rate than Relationship A. This graph represents Relationship A.
Which equations could represent Relationship B?
Select each correct answer.
Responses
y = 1.4x
y, = 1.4, x
y = 2.2x
y, = 2.2, x
y=12x
y equals 1 half x
y = 3x
y, = 3, x
First-quadrant graph showing a ray from the origin through the points begin ordered pair 2 comma 4 end ordered pair and begin ordered pair 4 comma 8 end ordered pair.
The equation that could represent Relationship B is:
y = 3x
Based on the information provided, the given equations that could represent Relationship B are:
y = 2.2x
y = 3x
Therefore, the correct answers are:
- y = 2.2x
- y = 3x
To determine which equations could represent Relationship B, we need to compare the rates of change of both Relationship A and Relationship B.
Relationship A is represented by a graph, but no specific equation is given. So, we cannot directly compare the rates of change. However, we can observe some information from the graph. According to the graph description, Relationship A has a first-quadrant graph showing a ray from the origin through the points (2, 4) and (4, 8). This means that as x increases by 1 from 2 to 4, y increases by 4 from 4 to 8. Therefore, the rate of change of Relationship A is 4/2 = 2.
Now we need to find equations that have a greater rate of change than 2, as Relationship B has a higher rate than Relationship A.
Let's compare each option:
1. y = 1.4x: The rate of change in this equation is 1.4, which is less than 2. So, this equation does not represent Relationship B.
2. y = 2.2x: The rate of change in this equation is 2.2, which is greater than 2. Therefore, this equation could represent Relationship B.
3. y = 12x: The rate of change in this equation is 12, which is much greater than 2. Therefore, this equation could represent Relationship B.
4. y = 3x: The rate of change in this equation is 3, which is greater than 2. Therefore, this equation could represent Relationship B.
Therefore, the equations that could represent Relationship B are:
- y = 2.2x
- y = 12x
- y = 3x
Note: The equations are written in slope-intercept form, where y is dependent on x.