a mobile phone company charges a fixed montly fee of $20 plus $0.10 per minute of calles.
1) write a linear equation to represent the total monthly cost y basd on the number of minutes x used (5 marks)
2) graph the equation abd use the graph to estimaete the monthly cost for 150 min of calls
3) explaion how the slope and y intercept related to the charges in this context

### 1) Linear Equation for Total Monthly Cost

To represent the total monthly cost $ y $ based on the number of minutes $ x $ used, we can set up a linear equation. 

The total cost is composed of two parts:
- A fixed monthly fee of $20.
- A variable cost of $0.10 per minute of calls.

So, the linear equation is:
\[
y = 0.10x + 20
\]
Where:
- $ y $ is the total monthly cost in dollars.
- $ x $ is the number of minutes of calls.

### 2) Graphing the Equation

To graph the equation $ y = 0.10x + 20 $:

1. **Plot the y-intercept (where $ x = 0 $)**: The y-intercept is $ y = 20 $, which represents the fixed monthly fee when no minutes are used.

2. **Plot another point**: For example, if $ x = 100 $ minutes:
   \[
   y = 0.10(100) + 20 = 10 + 20 = 30
   \]
   So, another point is (100, 30).

3. **Draw the line**: Connect the points to form a straight line, as it represents a linear relationship.

#### Estimating Monthly Cost for 150 Minutes
To estimate the monthly cost for 150 minutes using the graph:
- Locate $ x = 150 $ on the horizontal axis.
- Draw a vertical line up to the graph.
- Find the corresponding $ y $-value.

Alternatively, plug $ x = 150 $ directly into the equation:
\[
y = 0.10(150) + 20 = 15 + 20 = 35
\]
So, the estimated monthly cost for 150 minutes of calls is $35.

### 3) Interpretation of Slope and Y-Intercept

- **Slope (0.10)**: The slope represents the rate at which the total cost increases per minute of calls. In this context, for every additional minute of calls, the cost increases by $0.10.

- **Y-Intercept (20)**: The y-intercept represents the total cost when no minutes of calls are used. In this context, it reflects the fixed monthly fee of $20, which is the minimum amount charged regardless of call usage.

Would you like to go over any part of this, or dive deeper into any of the steps? Here are some related questions:

1. What would the equation look like if the fixed fee increased to $25?
2. How would the graph change if the per-minute charge was reduced to $0.05?
3. What is the monthly cost for 300 minutes of calls?
4. How would you interpret the graph if the fixed fee was $0 and only the per-minute charge applied?
5. What does a slope of 0.20 represent in a similar context?

**Tip:** When interpreting linear equations, remember that the slope indicates how much one variable changes with respect to the other, and the y-intercept gives the starting value of the dependent variable when the independent variable is zero.

a mobile phone company charges a fixed montly fee of $20 plus $0.10 per minute of calles. 1) write a linear equation to represent the total monthly cost y basd on the number of minutes x used (5 marks) 2) graph the equation abd use the graph to estimaete the monthly cost for 150 min of calls 3) explaion how the slope and y intercept related to the charges in this context

Learn how to calculate the total monthly cost of a mobile phone company based on a fixed fee and per-minute charge using a linear equation. Includes graphing the equation to estimate costs and understanding the relationship between slope and y-intercept in context. Suitable for Grades 7-9.

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