Question

Compare Linear Function 1 with Linear Function 2. Which one has the lesser initial value?

Linear function 1 : Lionel's cell phone plan cost $45 per month.
Linear function 2 : The relationship between the number of months Ruby has had her cell phone (x) and the total cost (y) is given by y = 40x + 60

Answer 1

To compare the initial values of Linear Function 1 and Linear Function 2, we need to identify the initial value (often the y-intercept) for each function.

1. **Linear Function 1**: This is based on a monthly cost of $45. Since this amount is constant and does not depend on any variable (like time), we can consider the initial value as simply $45.

2. **Linear Function 2**: This function is given by the equation \(y = 40x + 60\). Here, the initial value can be determined by evaluating the function when \(x = 0\):
\[
y = 40(0) + 60 = 60
\]
So, the initial value for Linear Function 2 is $60.

Now, we can compare the two initial values:
- Linear Function 1: $45
- Linear Function 2: $60

**Conclusion**: Linear Function 1 has the lesser initial value of $45 compared to Linear Function 2's initial value of $60.

Answer 2

you sure

Answer 3

Yes, I'm confident in the comparison of the initial values of the two linear functions as explained. Here’s a recap for clarity:

1. **Linear Function 1**: The cost is a flat rate of $45 per month. Since there are no additional charges or changes mentioned, we can take the initial cost (at \(x=0\)) to be $45.

2. **Linear Function 2**: The total cost \(y\) as a function of the number of months \(x\) is given by the equation \(y = 40x + 60\). When \(x = 0\), the total cost is:
\[
y = 40(0) + 60 = 60
\]
Therefore, the initial value (total cost when \(x=0\)) of Linear Function 2 is $60.

So, comparing both:
- Function 1 has an initial value of $45.
- Function 2 has an initial value of $60.

Thus, **Linear Function 1** indeed has the lesser initial value of $45.