for exercises 8-11, use the graph to answer the questions. the graph shows the amount of money that amir earns babysitting. 8. what is the slope of the line that connects the points shown? 9. what does the slope mean to amir? 10. what does amir earn when he babysits for 2.5 hours? 11. how many hours does amir have to babysit to earn $56? for exercises 12-14, use the description to answer the questions. stem connection environmentalists can compare the fuel efficiency of new cars by graphing the amount of gas used by the car in relation to the miles driven. 12. sketch the graph of a car that consumes a lot of gas to go a short distance. label this line “car a”. 13. sketch the graph of a car that consumes less gas than car a to go the same distance. label this line “car b”. 14. what do you notice about the slopes of the two lines? for exercise 15, answer the question. 15. find the error a student is graphing the distance that a car travels over time. he says that when the car travels at a slower speed, the graph changes to turn toward the x - axis with a negative slope. how do you respond to this student?

Question

Accepted Answer

### 8.
# Explanation:
## Step1: Identify two points
The two points on the graph are $(0.5,8)$ and $(1.5,24)$.
## Step2: Use slope - formula
The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $x_1 = 0.5,y_1 = 8,x_2=1.5,y_2 = 24$ into the formula: $m=\frac{24 - 8}{1.5 - 0.5}=\frac{16}{1}=16$.
# Answer:
$16$

### 9.
# Brief Explanations:
The slope represents the rate of change of the amount of money earned with respect to time. In the context of Amir's babysitting, it means Amir earns $16$ dollars per hour.
# Answer:
Amir earns $16$ dollars per hour babysitting.

### 10.
# Explanation:
## Step1: Use the linear - relationship
Since the slope is $16$ and we can assume the linear equation is $y=16x$ (where $y$ is the amount earned and $x$ is the number of hours).
## Step2: Substitute $x = 2.5$
When $x = 2.5$, $y=16	imes2.5 = 40$.
# Answer:
$40$ dollars

### 11.
# Explanation:
## Step1: Use the linear - equation
We know $y = 16x$, and we want to find $x$ when $y = 56$.
## Step2: Solve for $x$
Set up the equation $56=16x$. Then $x=\frac{56}{16}=3.5$.
# Answer:
$3.5$ hours

### 12.
# Brief Explanations:
A car that consumes a lot of gas to go a short distance has a high rate of gas - consumption. On a graph with gas used on the $y$ - axis and miles on the $x$ - axis, the line will have a steep positive slope. Start at the origin $(0,0)$ and draw a line with a steep upward - trend, and label it "Car A".
# Answer:
Draw a line with a steep positive slope starting from the origin and label it "Car A".

### 13.
# Brief Explanations:
A car that consumes less gas than Car A to go the same distance has a lower rate of gas - consumption. Draw a line with a less steep positive slope compared to Car A, starting from the origin, and label it "Car B".
# Answer:
Draw a line with a less steep positive slope than Car A, starting from the origin, and label it "Car B".

### 14.
# Brief Explanations:
The slope of the line represents the rate of gas - consumption. The line for Car A has a steeper slope, meaning it has a higher rate of gas - consumption, while the line for Car B has a less steep slope, indicating a lower rate of gas - consumption.
# Answer:
The slope of the line for Car A is steeper (greater) than the slope of the line for Car B, which means Car A has a higher gas - consumption rate.

### 15.
# Brief Explanations:
When a car travels at a slower speed, the distance it travels over time still increases, just at a slower rate. The graph of distance vs. time should still have a positive slope (since distance is increasing with time), but it will be less steep. The student is wrong because a negative slope would mean the distance is decreasing over time, which is not the case when the car is moving forward.
# Answer:
The student is incorrect. A slower - moving car still has a positive slope on a distance - time graph because the distance traveled is increasing over time, just at a slower rate. The slope should be positive but less steep than when the car is moving faster.

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QUESTION IMAGE

Question

Explanation:

8.

Step1: Identify two points

Step2: Use slope - formula

Step1: Use the linear - relationship

Step2: Substitute $x = 2.5$

Answer:

9.