Question

Diane's monthly bill for cell service can be computed using a linear equation. When she uses no data, the bill is $37.50. When she uses 2 GB of data, the bill is $45.50. a) What are the independent and dependent variable? b) If the linear equation is y=4x+37.50, what is the slope and y-intercept? c) What is Diane's bill be if she uses 5 GB of data in a month? d) If Diane's bill is $49.50, how much data did she use? Problem \#2 Olivia keeps track of the amount of time she works on homework each week and the number of problems she is able to solve. The data are shown in the table below. Create a scatter plot that accurately records the data? Be sure to label the chart

Answer 1

a) In the given scenario:
- Independent variable: The amount of data used (measured in GB)
- Dependent variable: Diane's monthly bill (measured in dollars)

b) The linear equation provided is y = 4x + 37.50. By comparing this equation with the standard form y = mx + b, we can identify the following:
- Slope (m): 4
- y-intercept (b): 37.50

c) To find Diane's bill if she uses 5 GB of data, we can substitute x = 5 into the linear equation and solve for y:
y = 4(5) + 37.50
y = 20 + 37.50
y = 57.50

Therefore, if Diane uses 5 GB of data in a month, her bill will be $57.50.

d) To find out how much data Diane used if her bill is $49.50, we can rearrange the linear equation to solve for x:
y = 4x + 37.50
49.50 = 4x + 37.50
12 = 4x
x = 3

Therefore, Diane used 3 GB of data if her bill is $49.50.

Problem #2: Olivia's Homework Data

Time (hours) | Number of Problems Solved |

| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
| 5 | 11 |

To create a scatter plot accurately representing the data, you can plot the values on a graph with the x-axis representing time (hours) and the y-axis representing the number of problems solved. Each point on the graph represents a pair of values from the table. Remember to label the chart with appropriate axis labels and a title to provide clarity.