Question

The table shows the grade, g, on a test when the number of problems, n, are correct. Write an equation to model the situation.

n:
10
18
21

g:
40
72
84

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since each grade is directly proportional to the number of problems correct, we can write the equation as:

g = k * n

where k is the constant of proportionality. To find k, we can pick any two sets of values for g and n and solve for k:

Using (n1,g1) = (10,40):
40 = k * 10
k = 40/10
k = 4

Now we can rewrite the equation with the value of k:

g = 4 * n

So the equation that models the situation is g = 4n.

Answer 2

The equation y=6x+6

describes the relationship between quantities x and y. Are the quantities in a proportional relationship?

A)Yes, because the graph of the equation is a straight line.

B)Yes, because the graph of the equation passes through the origin.

C)No, because the graph of the equation is not a straight line.

D)No, because the graph of the equation does not pass through the origin.

Answer 3

[AI-generated answer — Bot GPT 3.5]

The correct answer is C) No, because the graph of the equation is not a straight line.

For two quantities to be in a proportional relationship, the graph of the equation that describes their relationship must be a straight line that passes through the origin (0,0). In the given equation y = 6x + 6, the graph is a straight line but it does not pass through the origin. Therefore, the quantities x and y are not in a proportional relationship.

Answer 4

Which two ratios form a proportion?

1 over 2 and 8 over 4

2 over 1 and 16 over 8

1 over 2 and 4 over 2

2 over 1 and 4 over 8

Answer 5

[AI-generated answer — Bot GPT 3.5]

The two ratios that form a proportion are:

1 over 2 and 4 over 2

To determine if two ratios form a proportion, we need to check if their cross products are equal. In this case, the cross products for the given ratios are:

(1 * 2) = (4 * 2)
2 = 4

Since the cross products are equal, the ratios 1 over 2 and 4 over 2 form a proportion.

Answer 6

Which linear equation represents a non-proportional relationship?

y = x + 3

y = 4 over 5x

y = −3x

y = 1.5x

Answer 7

[AI-generated answer — Bot GPT 3.5]

The linear equation that represents a non-proportional relationship is:

y = x + 3

In a proportional relationship, the equation would be in the form y = kx, where k is a constant. However, in the equation y = x + 3, the coefficient of x is 1, which means that the relationship between y and x is not proportional.

Answer 8

In a second grade classroom, a student earns 25 stars for 5 compliments for good behavior. The teacher tracks the number of stars (y, vertical axis) and compliments (x, horizontal axis) on a graph. Which statements are correct? Choose more than 1 answer.

options:

A) Point (20, 100) represents earning 20 compliments.

B) Point (100, 20) represents earning 20 compliments.

C) Point (5, 1) represents the unit rate.

D) Point (1, 5) represents the unit rate.

E) Point (0, 50) represents the unit rate.

Answer 9

[AI-generated answer — Bot GPT 3.5]

The correct statements are:

A) Point (20, 100) represents earning 20 compliments.
C) Point (5, 1) represents the unit rate.

Here's the explanation for each statement:

A) Point (20, 100) represents earning 20 compliments:
In the given scenario, the student earns 25 stars for 5 compliments. This means that for every 5 compliments received, the student earns 25 stars. To find the number of stars earned for 20 compliments, we can use the unit rate of 5 compliments = 25 stars. Since 20 compliments is 4 times 5 compliments, multiplying the unit rate by 4 gives us 4 * 25 = 100 stars. So, the point (20, 100) represents earning 20 compliments.

C) Point (5, 1) represents the unit rate:
As mentioned above, the unit rate in this scenario is 5 compliments = 25 stars. Simplifying this ratio gives us 1 compliment = 5 stars. Therefore, the point (5, 1) represents the unit rate.

The other statements are not correct because they do not represent the scenario correctly or do not align with the given information.