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.

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.

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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