Question

A telephone company charges a fixed monthly rate plus a rate per minute of usage. The company charges $135 for 100 minutes of usage and $375 for 500 minutes of usage. An equation can be written to show the relationship between the total minutes used (x) and the total monthly charges (y). Which of the following best describes the steps to draw the graph of y against x?

Draw a graph which joins the points (135, 100) and (375, 500) and has a slope = 0.6
Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 0.6
Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 1.67
Draw a graph which joins the points (135, 100) and (375, 500) and has a slope = 1.67

Answer 1

Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 0.6

Explanation:

Data

x: total minutes used

y: total monthly charges

x | y

100 | $135

500 | $375

That can be expressed as coordinates (x, y), so the points are (100, 135) and (500, 375).

The slope is computed with two points (x2, y2) and (x1, y1) as follows:

slope = (y2 - y1)/(x2 - x1)

Replacing with data

slope = (375 - 135)/(500 - 100) = 0.6

Answer 2

Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 0.6

The ordered pairs are: (100, 135) and (500, 375)

The first number is the number of minutes of usage and the second number is the charge of the month.

The slope is: ( 375 -135) / (500 - 100) = 240/400 = 0.6