Determine if each answer choice represents a proportional or non-proportional linear relationship. Drag each answer choice to the correct column. The order does not matter.
Answer Choices:
A cellphone company charges $19.95 per month for the first 2G of data usage, then $5 per gig of usage over the initial 2G
y-intercept is not the origin
A cellphone company charges $29.95 per month for unlimited data usage.
Direct Variation
y = 5x + 1
y = -7x
y = x
4y = 2x
Proportional Linear Relationship:
A cellphone company charges $19.95 per month for the first 2G of data usage, then $5 per gig of usage over the initial 2G
Direct Variation
y = x
Non-Proportional Linear Relationship:
A cellphone company charges $29.95 per month for unlimited data usage.
y-intercept is not the origin
y = 5x + 1
y = -7x
4y = 2x
Proportional:
y = x
4y = 2x
Non-Proportional:
A cellphone company charges $19.95 per month for the first 2G of data usage, then $5 per gig of usage over the initial 2G
y-intercept is not the origin
A cellphone company charges $29.95 per month for unlimited data usage.
y = 5x + 1
y = -7x
Okay, what is a proportional linear relationship, and how is it different from proportional relationship?
A proportional linear relationship is a type of relationship where the ratio between the dependent and independent variables is always the same. In other words, the relationship between the two variables can be represented by a straight line that passes through the origin (0,0). The equation of a proportional linear relationship is y = kx, where k represents the constant of proportionality.
On the other hand, a proportional relationship is a broader concept that includes any relationship where the ratio between two quantities is constant. It does not necessarily have to be a linear relationship or pass through the origin.
To determine if each answer choice represents a proportional or non-proportional linear relationship, we need to analyze the equations given.
Let's go through each choice one by one:
1. A cellphone company charges $19.95 per month for the first 2G of data usage, then $5 per gig of usage over the initial 2G.
This relationship is non-proportional because there is a fixed cost ($19.95) plus an additional cost ($5 per gig) that is not directly proportional to the amount of data used. The cost increases as the amount of data used increases, but not at a constant rate.
2. y-intercept is not the origin.
This statement doesn't provide enough information about the relationship between variables. The y-intercept is the point where the line crosses the y-axis, and it being not the origin doesn't determine if the relationship is proportional or non-proportional.
3. A cellphone company charges $29.95 per month for unlimited data usage.
This relationship is non-proportional because there is a fixed cost ($29.95) regardless of the amount of data used. The cost remains the same, regardless of the amount of data used, making it a non-proportional relationship.
4. y = 5x + 1.
This relationship represents a proportional linear equation. It has a constant rate of change (slope) of 5, indicating that for every increase of 1 in x, y will increase by 5 units. This direct relationship indicates proportionality.
5. y = -7x.
This relationship represents a proportional linear equation. It has a constant rate of change (slope) of -7, indicating that for every increase of 1 in x, y will decrease by 7 units. This direct relationship indicates proportionality.
6. y = x.
This relationship represents a proportional linear equation. It has a slope of 1, indicating that for every increase of 1 in x, y will increase by 1 unit. This direct relationship indicates proportionality.
7. 4y = 2x.
This relationship represents a proportional linear equation. We can simplify the equation to y = (2/4)x, which can be further reduced to y = (1/2)x. This equation has a constant rate of change (slope) of 1/2, indicating that for every increase of 1 in x, y will increase by 1/2 unit. This direct relationship indicates proportionality.
So, based on the analysis above, the answer choices would be:
Proportional linear relationships:
- y = 5x + 1
- y = -7x
- y = x
- 4y = 2x
Non-proportional linear relationship:
- A cellphone company charges $19.95 per month for the first 2G of data usage, then $5 per gig of usage over the initial 2G.
Find the slope of the line represented by the table of values.
table:
y - -5, -2, 1, 4, 7
x - 10, 5, 0 -5, -10
A. 3/5
B. 5/3
C. -3/5
D. -5/3