**Graphing linear functions worksheet :**

Worksheet on graphing linear functions worksheet is much useful to the students who would like to practice solving real-world problems on linear functions.

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.

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.

**Problem 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.

After having gone through the stuff given above, we hope that the students would have understood "Graphing linear functions worksheet".

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