GRAPHING LINEAR FUNCTIONS

The table shows the total amount of rain that falls in various amounts of time during a heavy rain.

If 'x' denotes time and 'y' denotes total amount of rain, then the relationship between time and total amount of rain can be represented by the equation

y = 1.5x

The graph of the relationship will be a line, so the equation is a linear equation. Since there is exactly one value of y for each value of x, the relationship is a linear function.

Example 1 :

The temperature at dawn was 8 °F and increased steadily 2 °F every hour. The equation y = 2x + 8 gives the temperature y after x hours. State whether the relationship between the time and the temperature is proportional or non proportional. Then graph the function.

Solution :

Step 1 :

The given equation y = 2x + 8 is in slope-intercept form linear equation. That is, y = mx + b.

When we compare the equation y = 2x + 8 with y = mx + b, we get m = 2 and b = 8.

Therefore, the equation is a linear equation. Since b ≠ 0, the relationship is non proportional.

Step 2 :

Choose several values for the input x. Plug these values for x in the equation to find the output y.

x

0

2

4

6

2x + 8

2(0) + 8

2(2) + 8

2(4) + 8

2(6) + 8

y

8

12

16

20

(x, y)

(0, 8)

(2, 12)

(4, 16)

(6, 20)

Step 3 :

Graph the ordered pairs. Then draw a line through the points to represent the solutions of the function.

Problem 2 :

The temperature of a fish tank was 82 °F and decreased steadily 2 °F every hour. The equation y = -2x + 82 gives the temperature y after x hours. State whether the relationship between the time and the temperature is proportional or non proportional. Then graph the function.

Solution :

Step 1 :

The given equation y = -2x + 82 is in slope-intercept form linear equation. That is, y = mx + b.

When we compare the equation y = -2x + 82 with y = mx + b, we get m = -2 and b = 82.

Therefore, the equation is a linear equation. Since b ≠ 0, the relationship is non proportional.

Step 2 :

Choose several values for the input x. Plug these values for x in the equation to find the output y.

x

0

1

2

3

4

5

-2x + 82

-2(0) + 82

-2(1) + 82

-2(2) + 82

-2(3) + 82

-2(4) + 82

-2(5) + 82

y

82

80

78

76

74

72

(x, y)

(0, 82)

(1, 80)

(2, 78)

(3, 76)

(4, 74)

(5, 72)

Step 3 :

Graph the ordered pairs. Then draw a line through the points to represent the solutions of the function.

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