Question

A telephone company charges a fixed monthly rate plus a rate per megabytes of used company charges $120 for 100 megabytes of data and $95 for 50 equation can be written to show the relationship between the total of data used (x) and the total monthly charges (y).

Which of the following best describes the steps to draw the graph?
A) draw a graph that joins the points (100,120)and (50,95) and has a slope=0.50
B) draw a graph that joins the points (100,120) and (50,95) and has a slope=2
C) draws a graph that joins the points (120,100) and (95,50) and has a slope=2
D) draw a graph that joins the points (120,100)and (95,50)and has a slope=0.50​

Answer 1

To graph the relationship between monthly charges and data usage, a line should be drawn that joins the points (100, 120) and (50, 95) with a slope of 0.50 (Option A). The slope is calculated by dividing the change in cost by the change in data usage.

Step-by-step explanation:

To determine the correct steps to draw the graph representing the relationship between the total monthly charges (y) and the amount of data used (x), we need to find the fixed monthly rate plus the rate per megabyte, which constitutes the slope of our linear equation.

We are given two points: (100, 120) for 100 megabytes at $120, and (50, 95) for 50 megabytes at $95. To find the slope, we calculate the change in cost divided by the change in data usage, which gives us: (120 - 95) / (100 - 50) = 25 / 50 = 0.50. Thus, the slope is 0.50, and this line passes through the points (100, 120) and (50, 95).

Moreover, we know that when no data is used (x=0), there is still a charge. This base charge represents the y-intercept. If we apply the slope, we can calculate the y-intercept by extending the line to where it crosses the y-axis. The correct graph will join the points (100, 120) and (50, 95) and have a slope of 0.50, which is represented by Option A.