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4.3 Graphing Using Intercepts. An x-intercept of a graph is the x-coordinate of a point where the graph crosses the x-axis. An y-intercept of a graph is the y-coordinate of a point where the graph crosses the y-axis. Example 1 : Find the x-intercept and the

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Example 1 where the graph crosses the x-axis.: Find the x-intercept and the

y-intercept of the graph of 3x - 4y = 12.

  • To find the x-intercept, plug zero in for y and solve for x.

  • To find the y-intercept, plug zero in for x and solve for y.


3x - 4y = 12

x-intercept

3x – 4(0) = 12

3x = 12

x = 4

  • 3(0) – 4y= 12

  • -4y = 12

  • y = -3


  • Example 2 graph the equation 4x 8y 24 using the x and y intercepts
    Example 2 where the graph crosses the x-axis.: Graph the equation 4x + 8y =24 using the x and y-intercepts.

    • Find the x and y-intercepts.

    • Plot the x and y-intercepts and draw a line through them connecting them with a straight edge.

      4x + 8y =24

      x-intercept y-intercept

      x-int: 6 y-int: 3

      (6,0) (0,3)


    (0,3) where the graph crosses the x-axis.

    4x + 8y =24

    (6,0)


    Example 3 where the graph crosses the x-axis.: Identify the x-intercept and y-intercept

    of the graph.

    x-int: 2

    y-int: -4


    Example 4 where the graph crosses the x-axis.: You make and sell decorative bows. You sell small bows for $3 and large bows for $5. You want to earn $60 per week. This situation can be modeled by 3x + 5y = 60 where the x is the number of small bows and y is the number of large bows.

    a) Find the intercepts of the graph.

    b) Graph the equation.

    c) Give three possibilities for the number of

    each type of bow you can sell to earn $60.


    y-intercept where the graph crosses the x-axis.

    3(0) + 5y = 60

    5y = 60

    y = 12

    (0,12)

    3x + 5y = 60

    x-intercept

    3x + 5(0) = 60

    3x = 60

    x = 20

    (20,0)


    (0,12) where the graph crosses the x-axis.

    3x + 5y = 60

    (20,0)


    3x 5y 60
    3x + 5y = 60 where the graph crosses the x-axis.

    3x + 5(9) = 60

    3x + 45 = 60

    3x = 15

    x = 5

    (5, 9)

    3(10) + 5y = 60

    30 + 5y = 60

    5y = 30

    y = 6

    (10, 6)

    3(15) + 5y = 60

    45 + 5y = 60

    5y = 15

    y = 3

    (15, 3)

    1) 20 Small Bows , 0 Large Bows

    2) 0 Small Bows, 12 Large Bows

    3) 10 Small Bows, 6 Large Bows

    4) 15 Small Bows, 3 Large Bows

    5) 5 Small Bows, 9 Large Bows


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