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At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $2.40 and a 16-ounce cup costs $3.20.
Is the linear relationship between cup size and cost also proportional? Why or why not?
a) Yes, there is no constant of proportionality.
b) No, the constant of proportionality is 0.2.
c) Yes, the constant of proportionality is 0.2.
d) No, there is no constant of proportionality.
To determine if the relationship between cup size and cost is proportional, we need to check if there is a constant ratio between the cup size and the cost.
Let's calculate the cost per ounce for each cup size:
For the 12-ounce cup: $2.40 / 12 ounces = $0.20 per ounce
For the 16-ounce cup: $3.20 / 16 ounces = $0.20 per ounce
Since the cost per ounce is the same for both cup sizes ($0.20), the relationship is indeed proportional. The constant of proportionality in this case is 0.20.
Therefore, the correct answer is:
c) Yes, the constant of proportionality is 0.2.
Which linear equation shows a proportional relationship?
a) y equals negative 2 times x minus one fifth
b) y equals two thirds times x minus 1
c) y equals 4 times x plus 6
d) y equals three fourths times x
To determine which linear equation shows a proportional relationship, we need to look for the equation in the form of y = kx, where k is the constant of proportionality.
Let's analyze each equation:
a) y = -2x - 1/5: This equation does not show a proportional relationship since there is no constant term.
b) y = 2/3x - 1: This equation does not show a proportional relationship since the constant term is not zero.
c) y = 4x + 6: This equation does not show a proportional relationship since the coefficient of x is not a constant of proportionality.
d) y = 3/4x: This equation shows a proportional relationship since it is in the form y = kx, where k = 3/4.
Therefore, the linear equation that shows a proportional relationship is:
d) y = 3/4x
An indoor soccer field can be rented for personal use. The total cost for renting the field can be found by using the equation y = 225x. The x-variable is the number of hours the field is being rented, and the y-variable is the total cost, in dollars.
Which statement is true based on the given equation?
a) The equation shows a linear relationship, but not a proportional relationship.
b) The equation shows a linear relationship and a proportional relationship.
c) The equation does not show a linear relationship or a proportional relationship.
d) The equation shows a proportional relationship, but not a linear relationship.
Based on the given equation y = 225x, where x represents the number of hours the indoor soccer field is rented and y represents the total cost in dollars, we can see that this equation is in the form of y = kx, which is the form of a proportional relationship.
Therefore, the correct statement is:
b) The equation shows a linear relationship and a proportional relationship.
Which of the following tables represents a linear relationship that is also proportional?
x y
0 0
4 2
8 4
x y
0 1
2 3
4 5
x y
0 2
3 5
6 8
x y
0 3
6 5
12 7
To determine if a relationship is linear and proportional, we need to check if the ratio of y to x is constant for all data points.
Let's calculate the ratio of y to x for each table:
For the first table:
- At x=0, y=0, which gives us y/x = 0
- At x=4, y=2, which gives us y/x = 2/4 = 0.5
- At x=8, y=4, which gives us y/x = 4/8 = 0.5
Since the ratio of y to x is constant (0.5) for all data points in the first table, this table represents a linear relationship that is also proportional.
Therefore, the correct table is:
x y
0 0
4 2
8 4
Which linear graph represents a proportional relationship?
a) A graph of a straight line that passes through the points negative 1 comma 3 and 0 comma 0.
b) A graph of a straight line that passes through the points negative 4 comma negative 3 and 0 comma negative 2.
c) A graph of a straight line that passes through the points negative 1 comma 3 and 0 comma 3.
d) A graph of a straight line that passes through the points negative 2 comma negative 1 and negative 2 comma 0.