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. 

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

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

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

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6