**Determine if a function is linear worksheet :**

Worksheet on determine if a function is linear is much useful to the students who would like to practice problems on describing functions.

1. A square tile has a side length of x inches. The equation y = x² gives the area of the tile in square inches. Determine whether the relationship between x and y is linear and, if so, if it is proportional.

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 linear, if so, if it is proportional.

**Problem 1 :**

A square tile has a side length of x inches. The equation aaa y = x² gives the area of the tile in square inches. Determine whether the relationship between x and y is linear and, if so, if it is proportional.

**Solution : **

**Step 1 :**

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

**x**

1

2

3

4

**x²**

1²

2²

3²

4²

**y**

1

4

9

16

**(x, y)**

(1, 1)

(2, 4)

(3, 9)

(4, 16)

**Step 2 :**

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

**Step 3 : **

Describe the relationship between x and y.

The graph is not a line. So the relationship between the side length of the square and its area is non linear.

Only a linear relationship can be proportional. Since the relationship is non linear, it is not proportional.

**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 linear, if so, if it is proportional.

**Solution : **

**Step 1 :**

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 2 :**

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

**Step 3 :**

Describe the relationship between x and y.

The graph is a line. So the relationship between the time and the temperature is linear.

But the line is not passing through the origin. So, it is not proportional.

**Note : **

The graphs of all linear relationships will be a line. If the line passes through the origin, the linear relationship is proportional.

If the line does not pass through the origin, the linear relationship is non proportional.

After having gone through the stuff given above, we hope that the students would have understood "Determine if a function is linear worksheet".

Apart from the stuff given above, if you want to know more about "Determining whether a function is linear", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**