An electrician charges a $50 service fee plus $40 per hour of work.

If x represents the time in hours and y represents the total amount charged, what points will fall on the graph of this relationship?

Select TWO correct answers.
A.(0, 40)
B.(2, 130)
C.(2.5, 140)
D.(3, 190)
E.(3.5, 190)

The relationship between the total amount charged $ y $ and the time worked in hours $ x $ can be expressed as a linear equation:

\[
y = 50 + 40x
\]

Where:
- $ 50 $ is the fixed service fee.
- $ 40x $ represents the additional charge based on the number of hours worked, at a rate of $40 per hour.

Now, let's evaluate each option by substituting the $ x $ values into the equation and checking if the corresponding $ y $ value is correct.

### A. (0, 40)
Substitute $ x = 0 $ into the equation:

\[
y = 50 + 40(0) = 50
\]

The point is $ (0, 50) $, **not** $ (0, 40) $. So, **A is incorrect**.

### B. (2, 130)
Substitute $ x = 2 $ into the equation:

\[
y = 50 + 40(2) = 50 + 80 = 130
\]

The point is $ (2, 130) $, which is **correct**.

### C. (2.5, 140)
Substitute $ x = 2.5 $ into the equation:

\[
y = 50 + 40(2.5) = 50 + 100 = 150
\]

The point is $ (2.5, 150) $, **not** $ (2.5, 140) $. So, **C is incorrect**.

### D. (3, 190)
Substitute $ x = 3 $ into the equation:

\[
y = 50 + 40(3) = 50 + 120 = 170
\]

The point is $ (3, 170) $, **not** $ (3, 190) $. So, **D is incorrect**.

### E. (3.5, 190)
Substitute $ x = 3.5 $ into the equation:

\[
y = 50 + 40(3.5) = 50 + 140 = 190
\]

The point is $ (3.5, 190) $, which is **correct**.

### Correct Answers: 
The two points that fall on the graph are:

**B. (2, 130)** and **E. (3.5, 190)**.

Would you like more details or have any further questions?

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Here are 5 related questions:
1. What would be the total charge if the electrician worked for 4 hours?
2. How can you determine the slope of this linear equation?
3. What does the $ y $-intercept represent in this context?
4. If the electrician gives a $20 discount on the service fee, how would the equation change?
5. What is the total charge after 1.5 hours of work?

**Tip**: When solving linear equations, always check the units for the slope and intercept to ensure you correctly interpret the problem context.

Discover how to determine points on the graph of a linear equation that models an electrician's service fee of $50 and an hourly rate of $40. Evaluate different options to find the correct points, suitable for students in Grades 6-8.

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