Question

A cab company charges $12 per mile for a lift to the airport.

What change would the company make to their charges to make this a non proportional situation?

(1 point)
Responses

Charge $15 per mile instead of $12

No changes are needed.
No changes are needed.

Charge a flat rate of $20 and then $12 per mile
Charge a flat rate of $20 and then $12 per mile

Charge $4 per mile instead of $12

Answer 1

One business charges $22 per t-shirt that is custom made.

Another business charges $16 per t-shirt plus a $15 set up fee for custom made t-shirts.

How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph?

(1 point)
Responses

Left 15
Left 15

Down 15
Down 15

Up 15
Up 15

Down 4
Down 4

Up 4
Up 4

Right 4

Answer 2

Solve this equation for y: 7y=12x
(1 point)
Responses

y=127x
y is equal to 12 sevenths x

y=12x−7
y is equal to 12 x minus 7

y=12x+7
y is equal to 12 x plus 7

y=712x

Answer 3

Change the equation from standard form to slope-intercept form by solving for y.

8x−4y=24

Determine who changed the equation correctly:

Bob:

Subtract 8x from both sides: −4y=−8x+24

Divide by -4 on both sides: y=2x−6

Bill:

Subtract 8x from both sides: −4y=16x

Divide by -4 on both sides: y=−4x

Bud:

Subtract 8x from both sides: −4y=−8x+24

Divide by -4 on both sides: y=2x+24



(1 point)
Responses

None of them are correct
None of them are correct

Bud
Bud

Bob
Bob

Bill

Answer 4

Solve 3x+2b=6c
for x.

Step 1: 3x+2b−2b=6c−2b
subtract 2b from both sides

Step 2: 3x=6c−2b
combine like terms/simplify

Step 3: 3x3=6c3−2b
divide by 3 on both sides to get x isolated

Step 4: x=2c−2b
simplify/final answer

Which statement is TRUE?

(1 point)
Responses

The process has an error. The correct answer is x=−4b−c
The process has an error. The correct answer is x is equal to negative 4 b minus c

The process is correct.
The process is correct.

The process has an error. The correct answer is x=2c−23b
The process has an error. The correct answer is x is equal to 2 c minus 2 thirds b

The process has an error. The correct answer is x=4bc3

Answer 5

Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. The river was 60 feet before the drought began.(4 points)
a. What is the rate of change (slope) for this scenario? (Response area)

b. What is the y-intercept for this scenario? (Response area)

c. Write an equation for the scenario in slope-intercept form. (Response area)

d. Write an equation in standard form. (response area)

responses
(-5, 0)
y = -5x -35
5x + y =35
y = -5x + 60
-5x + y = 60
-5
15
(0, -5)
(0, 60)
5x + y = 60
5
y = 5x + 45

Answer 6

To make the cab company's charges a non-proportional situation, they need to introduce a fixed charge that does not depend on the distance traveled. Currently, charging $12 per mile is a proportional relationship, as the cost increases directly with the number of miles.

Among the options provided, the response that introduces a fixed charge is:

**Charge a flat rate of $20 and then $12 per mile.**

This setup introduces a flat fee of $20, making the overall cost a combination of a fixed charge and a variable charge based on distance, thus creating a non-proportional relationship.

Answer 7

To transform the first graph (which represents a proportional relationship of $22 per t-shirt) into a non-proportional graph with the same y-intercept as the second graph (which has a set-up fee of $15 plus $16 per t-shirt), you need to introduce a fixed cost.

The second business has a y-intercept of $15 because of the set-up fee. The first business has a y-intercept of $0, as there are no fixed fees.

To align the y-intercept of the first graph with that of the second graph, you would need to move the first graph down by $15. This effectively means when there are no t-shirts ordered, the cost would start at $15 (the same as the second business when only considering the set-up fee).

Therefore, the correct response is:

**Down 15.**

Answer 8

To solve the equation \(7y = 12x\) for \(y\), we isolate \(y\) by dividing both sides by 7:

\[
y = \frac{12x}{7}
\]

This can be expressed as:

\[
y = \frac{12}{7}x
\]

So, the correct response would be:

**y is equal to 12 sevenths x.**

Answer 9

Let's solve the equation \(8x - 4y = 24\) step by step to see who made the correct changes.

1. Start with the original equation:
\[
8x - 4y = 24
\]

2. Subtract \(8x\) from both sides:
\[
-4y = -8x + 24
\]

3. Next, divide both sides by \(-4\):
\[
y = \frac{-8x}{-4} + \frac{24}{-4}
\]
Simplifying gives:
\[
y = 2x - 6
\]

Now let's evaluate each person's solution:

- **Bob:**
- Subtracts \(8x\) correctly: \(-4y = -8x + 24\) (correct so far)
- Divides by \(-4\) correctly: \(y = 2x - 6\) (correct)

- **Bill:**
- Subtracts \(8x\) incorrectly: \(-4y = 16x\) (incorrect)

- **Bud:**
- Subtracts \(8x\) correctly: \(-4y = -8x + 24\) (correct so far)
- Divides by \(-4\) incorrectly: \(y = 2x + 24\) (incorrect)

Based on this analysis, the correct solution is given by **Bob**.

So the final answer is:

**Bob**.

Answer 10

Let's go through the steps provided and solve the equation \(3x + 2b = 6c\) for \(x\).

1. **Step 1: Subtract \(2b\) from both sides:**
\[
3x + 2b - 2b = 6c - 2b
\]
This simplifies to:
\[
3x = 6c - 2b
\]

2. **Step 2: Combine like terms/simplify:**
This has already been simplified correctly in Step 1, so we proceed to the next step.

3. **Step 3: Divide by 3 on both sides:**
\[
\frac{3x}{3} = \frac{6c - 2b}{3}
\]
This simplifies to:
\[
x = \frac{6c - 2b}{3}
\]

4. **Step 4: Further simplify:**
Break down the fraction:
\[
x = \frac{6c}{3} - \frac{2b}{3}
\]
Which simplifies to:
\[
x = 2c - \frac{2}{3}b
\]

So the final answer is:
\[
x = 2c - \frac{2}{3}b
\]

Looking at the options provided:

1. **The process has an error. The correct answer is \(x = -4b - c\)**
2. **The process has an error. The correct answer is \(x\) is equal to negative \(4b\) minus \(c\)**
3. **The process is correct.**
4. **The process has an error. The correct answer is \(x = 2c - \frac{2}{3}b\)**
5. **The process has an error. The correct answer is \(x = \frac{4bc}{3}\)**

The correct final answer derived from the steps taken is \(x = 2c - \frac{2}{3}b\), which matches the 4th response.

Therefore, the true statement is:

**The process has an error. The correct answer is \(x = 2c - \frac{2}{3}b\).**

Answer 11

To analyze the water level change of the river over time, we can follow these steps:

### a. What is the rate of change (slope) for this scenario?

We can find the slope using the two data points given:

1. Point 1: \( (3, 45) \) — after 3 days, the water level is 45 feet.
2. Point 2: \( (10, 10) \) — after 10 days, the water level is 10 feet.

The formula for the slope (rate of change) \( m \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in the values:

\[
m = \frac{10 - 45}{10 - 3} = \frac{-35}{7} = -5
\]

So, the rate of change (slope) is:

**-5**

### b. What is the y-intercept for this scenario?

The y-intercept is the value of \( y \) when \( x = 0 \). According to the problem, the water level was **60 feet** before the drought began (at \( t = 0 \)).

So, the y-intercept is:

**(0, 60)**

### c. Write an equation for the scenario in slope-intercept form.

Using the slope \( m = -5 \) and the y-intercept \( (0, 60) \), we can write the equation in slope-intercept form \( y = mx + b \):

\[
y = -5x + 60
\]

### d. Write an equation in standard form.

To convert \( y = -5x + 60 \) to standard form \( Ax + By = C \), we can rearrange the equation:

1. Add \( 5x \) to both sides:
\[
5x + y = 60
\]

So, the equation in standard form is:

**5x + y = 60**

### Summary of Responses:
a. \(-5\)
b. \((0, 60)\)
c. \(y = -5x + 60\)
d. \(5x + y = 60\)