Employee 1 - Earnings per Hour Employee 2 - Earnings per Hour

Question

(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 $10 per hour and Employee 2 earns $15 per hour.

Answer 1

To determine which employee earns more per hour, we need to calculate the earnings per hour for each employee based on the data provided.

For Employee 1:

1. At (0, 0): Earnings = 0, Hours = 0 (undefined, skip)
2. At (30, 2): Earnings = 30, Hours = 2 → Earnings per hour = \( \frac{30}{2} = 15 \)
3. At (45, 3): Earnings = 45, Hours = 3 → Earnings per hour = \( \frac{45}{3} = 15 \)
4. At (60, 4): Earnings = 60, Hours = 4 → Earnings per hour = \( \frac{60}{4} = 15 \)

So, Employee 1 earns $15 per hour on average.

For Employee 2:

1. At (0, 0): Earnings = 0, Hours = 0 (undefined, skip)
2. At (30, 3): Earnings = 30, Hours = 3 → Earnings per hour = \( \frac{30}{3} = 10 \)
3. At (40, 4): Earnings = 40, Hours = 4 → Earnings per hour = \( \frac{40}{4} = 10 \)
4. At (50, 5): Earnings = 50, Hours = 5 → Earnings per hour = \( \frac{50}{5} = 10 \)

So, Employee 2 earns $10 per hour on average.

Comparison:

• Employee 1 earns $15 per hour.
• Employee 2 earns $10 per hour.

Therefore, Employee 1 earns more per hour.

None of the options exactly match this conclusion, but based on the closest information, the answer is:

B. Employee 1, because Employee 1 earns $15 per hour and Employee 2 earns $30 per hour.

(You may need to adjust the reasoning as the stated earnings for Employee 2 seems incorrect in option B.)

Answer 2

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 3

To find the equation of the line given two points, we can use the slope-intercept form of the equation of a line, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

We have two points:

1. Point A: \( (1, 0) \)
2. Point B: \( (0, -3) \)

Step 1: Calculate the slope \(m\)

The slope \(m\) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let's assign point A as \((x_1, y_1)\) = \( (1, 0) \) and point B as \((x_2, y_2)\) = \( (0, -3) \): \[ m = \frac{-3 - 0}{0 - 1} = \frac{-3}{-1} = 3 \]

Step 2: Use one point to solve for \(b\)

Now that we have the slope \(m = 3\), we can plug it into the slope-intercept form \(y = mx + b\) using either of the points. We can use point B \( (0, -3) \): \[ -3 = 3(0) + b \] \[ -3 = b \]

Step 3: Write the equation

Now we have \(m = 3\) and \(b = -3\), so the equation of the line is: \[ y = 3x - 3 \]

Now, looking at the provided options:

• a. \(y = 3x + 3\)
• b. \(-3x - y = 3\) (rewritten as \(y = -3x - 3\))
• c. \(y = -3x - 3\)
• d. \(y = 3x - 3\)

The correct answer is: d. \(y = 3x - 3\).

Answer 4

Transform 4x + y = -12 to slope-intercept form.

a. 4x + y + 12 = 0
b. y = 4x - 12
c. y = -4x - 12
d. y = 3/x

Answer 5

To transform the equation \(4x + y = -12\) into slope-intercept form (which is \(y = mx + b\)), we need to solve for \(y\).

Starting with the equation: \[ 4x + y = -12 \]

Step 1: Isolate \(y\)

Subtract \(4x\) from both sides: \[ y = -4x - 12 \]

Now we have the equation in slope-intercept form.

Step 2: Identify \(m\) and \(b\)

From the equation \(y = -4x - 12\):

• The slope \(m\) is \(-4\)
• The y-intercept \(b\) is \(-12\)

Now we can match this with the provided options.

• a. \(4x + y + 12 = 0\) (not in slope-intercept form)
• b. \(y = 4x - 12\) (incorrect slope)
• c. \(y = -4x - 12\) (correct!)
• d. \(y = \frac{3}{x}\) (not linear)

The correct answer is: c. \(y = -4x - 12\).