Question

The graph displays the number of miles a car traveled and the gallons of gasoline used. Determine the average miles per gallon.

A. The car averaged 4,500 miles per gallon.
B. The car averaged 15 miles per gallon.
C. The car averaged 300 miles per gallon.
D. The car averaged 20 miles per gallon.

Answer 1

To determine the average miles per gallon (MPG), you need to divide the total number of miles traveled by the total gallons of gasoline used. However, since the specific graph you referred to is not visible, I can't provide the exact calculation.

Here's how you can calculate it if you have the values:

1. **Find the total miles driven:** Look at the total number of miles from the graph.
2. **Find the total gallons used:** Look at the total number of gallons used from the graph.
3. **Use the formula:**
\[
\text{MPG} = \frac{\text{Total Miles}}{\text{Total Gallons}}
\]

Once you have calculated MPG, you can select the correct option from A, B, C, or D.

Please provide the specific numbers from the graph for accurate help!

Answer 2

Employee 1 - Earnings per Hour Employee 2 - Earnings per Hour
(0, 0) (0, 0)
(30, 2) (30, 3)
(45, 3) (40, 4)
(60, 4) (50, 5)

Two employees tracked their earnings and hours that they worked. The graphs document the earnings for Employee 1 and Employee 2. Which employee earns more per hour?

A. Employee 1, because Employee 1 earns $30 per hour and Employee 2 earns $10 per hour.
B. Employee 1, because Employee 1 earns $15 per hour and Employee 2 earns $30 per hour.
C. Employee 2, because Employee 1 earns $15 per hour and Employee 2 earns $30 per hour.
D. Employee 2, because Employee 1 earns $10 per hour and Employee 2 earns $15 per hour.

Answer 3

To determine which employee earns more per hour, we can find the earnings per hour for both employees at the data points provided.

### Earnings Calculation:
1. **Employee 1 Earnings per Hour:**
- At (0, 0): Earnings = $0/hour (0 / 0)
- At (30, 2): Earnings = \( \frac{30}{2} = 15\) dollars/hour
- At (45, 3): Earnings = \( \frac{45}{3} = 15\) dollars/hour
- At (60, 4): Earnings = \( \frac{60}{4} = 15\) dollars/hour

**Average Rate for Employee 1:** 15 dollars/hour

2. **Employee 2 Earnings per Hour:**
- At (0, 0): Earnings = $0/hour (0 / 0)
- At (30, 3): Earnings = \( \frac{30}{3} = 10\) dollars/hour
- At (40, 4): Earnings = \( \frac{40}{4} = 10\) dollars/hour
- At (50, 5): Earnings = \( \frac{50}{5} = 10\) dollars/hour

**Average Rate for Employee 2:** 10 dollars/hour

### Conclusion:
- **Employee 1 earns $15 per hour**.
- **Employee 2 earns $10 per hour**.

Therefore, the correct choice is **C. Employee 2, because Employee 1 earns $15 per hour and Employee 2 earns $30 per hour** is incorrect.

Since the provided options are not entirely accurate based on the calculations, recheck or clarify the values against the calculations provided here.

The correct conclusion based on the average earnings per hour would be:

**Employee 1 earns more per hour compared to Employee 2.**

Answer 4

(0, 0)
(1, -3)
(2, -6)
(3, -9)

What is the slope of the line?

A. -6
B. -1
C. -3
D. 3

Answer 5

To find the slope of the line given the points \((0, 0)\), \((1, -3)\), \((2, -6)\), and \((3, -9)\), we can use the formula for the slope \( m \):

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

Let's calculate the slope using the first two points \((0, 0)\) and \((1, -3)\):

- \((x_1, y_1) = (0, 0)\)
- \((x_2, y_2) = (1, -3)\)

Substituting into the slope formula:

\[
m = \frac{-3 - 0}{1 - 0} = \frac{-3}{1} = -3
\]

Now, let's verify the slope using another pair of points, such as \((1, -3)\) and \((2, -6)\):

- \((x_1, y_1) = (1, -3)\)
- \((x_2, y_2) = (2, -6)\)

Substituting into the slope formula:

\[
m = \frac{-6 - (-3)}{2 - 1} = \frac{-6 + 3}{1} = \frac{-3}{1} = -3
\]

The slope remains consistent across different pairs of points. Thus, the slope of the line is \(-3\).

The correct answer is **C. -3**.

Answer 6

What can be said about two lines with equations y = 5x + 10 and y = 5x - 5?

a. the lines have different slopes but the same y-intercepts.
b. the lines are parallel.
c. one line is rising while the other line is moving downward.
d. the lines intersect.

Answer 7

To analyze the two given lines with equations \( y = 5x + 10 \) and \( y = 5x - 5 \), we can compare their slopes and y-intercepts.

### Analyzing the Equations
1. **First line:** \( y = 5x + 10 \)
- Slope: \( 5 \)
- Y-intercept: \( 10 \)

2. **Second line:** \( y = 5x - 5 \)
- Slope: \( 5 \)
- Y-intercept: \( -5 \)

### Comparison
- **Slopes:** Both lines have the same slope of \( 5 \).
- **Y-intercepts:** The first line has a y-intercept of \( 10 \), while the second line has a y-intercept of \( -5 \).

### Conclusion
Since the slopes are equal and the y-intercepts are different, the two lines are parallel. They will never intersect.

### Answer
The correct option is **b. the lines are parallel.**

Answer 8

Use the graph to answer the question.
(1,0)
(0,-3)

What is the equation of the line in the form y = mx + b?

a. y = 3x + 3
b. -3x - y = 3
c. y = -3x - 3
d. y = 3x -3

Answer 9

To determine the equation of the line that passes through the points \((1, 0)\) and \((0, -3)\), we can follow these steps:

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's assign the points:
- \((x_1, y_1) = (1, 0)\)
- \((x_2, y_2) = (0, -3)\)

Substituting in:
\[
m = \frac{-3 - 0}{0 - 1} = \frac{-3}{-1} = 3
\]

2. **Use the slope-intercept form (y = mx + b)**:
Now that we have the slope \(m = 3\), we can use one of the points to find the y-intercept \(b\). Use point \((0, -3)\):
\[
-3 = 3(0) + b \implies b = -3
\]

3. **Write the equation**:
Now we can write the equation of the line:
\[
y = 3x - 3
\]

### Conclusion
The equation of the line in the form \(y = mx + b\) is:
**d. \(y = 3x - 3\)**.

Answer 10

Graph the linear equation y = -6x - 4.

a. (1, 2) & (0, -4)
b. (3, 0) & (0, -2)
c. (0, -4) & (1, -10)
d. (0, 2) & (1, -1)

Answer 11

To graph the linear equation \(y = -6x - 4\), we can identify some key points by substituting different values for \(x\) and calculating the corresponding \(y\) values.

### Calculate Points
1. **When \(x = 0\):**
\[
y = -6(0) - 4 = -4
\]
Point: \((0, -4)\)

2. **When \(x = 1\):**
\[
y = -6(1) - 4 = -6 - 4 = -10
\]
Point: \((1, -10)\)

3. **When \(x = -1\):**
\[
y = -6(-1) - 4 = 6 - 4 = 2
\]
Point: \((-1, 2)\)

### Summary of Points
From the calculations:
- **Point 1:** \((0, -4)\)
- **Point 2:** \((1, -10)\)

### Match with Options
Now we can compare these points with the given options.

- **a. (1, 2) & (0, -4)** — does not match (1, 2) is not correct.
- **b. (3, 0) & (0, -2)** — does not match.
- **c. (0, -4) & (1, -10)** — matches perfectly.
- **d. (0, 2) & (1, -1)** — does not match.

### Conclusion
The correct option based on the calculations is:
**c. (0, -4) & (1, -10)**.