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4.3 Graphing Using Intercepts

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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

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.

- y-intercept

3x - 4y = 12

x-intercept

3x – 4(0) = 12

3x = 12

x = 4

- 3(0) – 4y= 12

- 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)

4x + 8y =24

(6,0)

Example 3: Identify the x-intercept and y-intercept

of the graph.

x-int: 2

y-int: -4

Example 4: 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

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)

3x + 5y = 60

(20,0)

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