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Group C. Section P.2. How to Sketch the Graph of an Equation. Graph of Equation: The set of all solution points of an equation Rewrite the equation so that one of the variables is isolated on one side Make a table of several solution points Plot these points in the C artesian plane

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Section P.2

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Group c

Group C

Section P.2


How to sketch the graph of an equation

How to Sketch the Graph of an Equation

  • Graph of Equation: The set of all solution points of an equation

  • Rewrite the equation so that one of the variables is isolated on one side

  • Make a table of several solution points

  • Plot these points in the Cartesian plane

  • Connect the points with a smooth curve


Example 1

Example 1

First, make a table of values by choosing values of x and calculating the values of y

Now plot the corresponding points


Using a graphing utility

Using a Graphing Utility

  • Rewrite the equation so y is isolated

  • Enter the equation into the utility

  • Determine a viewing window that shows all important features of the graph

  • Graph equation


Example 2 sketching a circle using a graphing utility

Example 2: Sketching a Circle Using a Graphing Utility

  • The graph of x2 + y2 = 9 is a circle whose center is at the origin and radius is 3. To graph the equation, solve for y.

  • x2 + y2 = 9

  • y2 = 9 - x2

  • y = √9 - x2

  • The graph of y = √9 - x2 is the top half

  • The graph of y = -√9 - x2 is the bottom half


X 2 y 2 9

x2 + y2 = 9

Enter both equations into the calculator and generate the graph. If you use the standard viewing window the graph may not appear to be a circle, by changing the viewing window to a square setting you can overcome this.


Example 3 real life

Example 3: Real life

  • A runner runs a constant rate of 4.9 mph. (Distance = Rate x Time)

  • d = 4.9t

  • Determine how far a runner can run in 3.1 hours

  • How long will it take to run a 26.2 mile marathon?


Example 3 real life1

Example 3: Real life

  • Substitute 3.1 hours for t

    • d = 4.9(3.1)

    • d = 15.2 miles

    • In 3.1 hours the runner could run 15.2 miles

  • d = Rt

    • d/R = t

    • 26.2m / 4.9mph = t

    • t = 5.3 hours

  • It would take about 5.3 hours to run a 26.2 mile marathon


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