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 electrician charges a $50 service fee plus $40 per hour of work. The equation that represents this relationship is:

\[
y = 50 + 40x
\]
where:
- $ y $ is the total amount charged.
- $ x $ is the number of hours worked.

Now, let's check which points satisfy this equation.

### Option A: (0, 40)
Substitute $ x = 0 $ into the equation:
\[
y = 50 + 40(0) = 50
\]
The point (0, 40) does **not** fall on the graph, because when $ x = 0 $, $ y = 50 $, not 40. So, **A is incorrect**.

### Option B: (2, 130)
Substitute $ x = 2 $ into the equation:
\[
y = 50 + 40(2) = 50 + 80 = 130
\]
The point (2, 130) is correct. So, **B is correct**.

### Option C: (2.5, 140)
Substitute $ x = 2.5 $ into the equation:
\[
y = 50 + 40(2.5) = 50 + 100 = 150
\]
The point (2.5, 140) does **not** fall on the graph, because when $ x = 2.5 $, $ y = 150 $, not 140. So, **C is incorrect**.

### Option D: (3, 190)
Substitute $ x = 3 $ into the equation:
\[
y = 50 + 40(3) = 50 + 120 = 170
\]
The point (3, 190) does **not** fall on the graph, because when $ x = 3 $, $ y = 170 $, not 190. So, **D is incorrect**.

### Option E: (3.5, 190)
Substitute $ x = 3.5 $ into the equation:
\[
y = 50 + 40(3.5) = 50 + 140 = 190
\]
The point (3.5, 190) is correct. So, **E is correct**.

### Final Answer:
The two correct points are:
- **B. (2, 130)**
- **E. (3.5, 190)**

Would you like more details on this?

Here are 5 related questions to expand on this problem:
1. How would the equation change if the service fee increased to $60?
2. What would be the total charge for 5 hours of work?
3. How would the graph of this equation look like on a coordinate plane?
4. What does the slope of the equation represent in this context?
5. How can we determine the service fee just by looking at the equation?

**Tip:** The y-intercept of the equation gives the fixed starting charge, which in this case is the service fee.

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)

Determine which points fall on the graph of the linear equation representing an electrician's charges with a $50 service fee and $40 per hour rate. Learn how to apply linear equations and coordinate geometry concepts. Suitable for students in Grades 6-8.

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