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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

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masterofcheese04
The correct answer to this question is letter "B. Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 0.6." The one on the x axis should be the number of minutes and on the other hand, the one on the y axis should be the amount being charged.
ezequielburela

Answer:

The graph which describes the relationship between company charges and minutes of usage is the graph containing the points (100,135) and (500,375) and has a slope of 0.6. Where the first coordinate of the points are the minutes and the second coordinate the charges.

Step-by-step explanation:

As the first coordinate of a point always represents the x variable and the second coordinate they value, the possible options to describes this situation are:

  • The graph join which joins the points (100,135) and (500,375) and has a slope =0.6
  • The graph join which joins the points (100,135) and (500,375) and has a slope =1.6

The other options are not possible since the order of the coordinates is inverted.  

One of the possibilities showing above must be rejected since one have the incorrect slope. To verify the correct slope we calculate the variation of y coordinates and divide by the variation of x coordinates:

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

Assuming the point named '2' as the point (100,135) and the point named '1' as (500,375):

[tex]m=\frac{(375-135) \$}{(500-100) minutes}[/tex]

[tex]m=\frac{(240) \$}{(400) minutes}[/tex]

[tex]m=0.6 \$/minutes[/tex]

Thus, that the graph joining the points (100,135) and (500,375) and has a slope of 0.6 the only possible action.