# INTERPRETING GRAPHS

In this section, we are going to see, how to describe a relationship between two variables x and y by interpreting the graph.

Example  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 rate of change between the side length and area of a square is constant using the graph. And also describe whether the relationship between the two variables is linear.

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 straight line. So the rate of change between the side length and area of a square is not constant.

Only a straight line graph will represent a linear relationship. Since the graph is not a straight line, the relationship between the two variables x and y is non linear.

Example  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. Determine whether the rate of change between the time and temperature is constant. And also describe whether the relationship between the two variables is linear.

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 :

Since the graph is a straight line, the rate of change between the  time and temperature is constant.

Since the rate of change is constant and the graph is a straight line, the relationship between the two variables x and y is linear.

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