Lines and the Coordinate Plane: Graphing the Equation of a Line

Solving Problems

Lines and graphs have many real-world applications.  See the example below for more information about how to use linear graphs to solve problems.

Example

The text messaging rates of a cell phone company are graphed below.

graph showing pricing for text messages

  1. What is the y-intercept?  What does it represent?

    The y-intercept is 5.  This means that it costs 5 to send 0 messages.  This is the initial rate for the plan.
     
  2. What is the slope?  What does it represent?

    m equals 10 minus 5 divided by 50 minus 0, m equals 5 divided by 50, m equals one-tenth

    The slope is .1, which is 10 cents.  The rate is 10 cents per message.
     
  3. What is the equation of the line?

    m = 0.1, b = 5
    y = 0.1x + 5
     
  4. Use the equation to determine the cost of sending 100 messages.

    y = 0.1x + 5
    y = 0.1(100) + 5
    y = 10 + 5
    y = 15