Proportional and non proportional graphs :
If a relationship is nonlinear, it is nonproportional. If it is linear, it may be either proportional or nonproportional. When the graph of the linear relationship contains the origin, the relationship is proportional.
A linear equation is an equation whose solutions are ordered pairs that form a line when graphed on a coordinate plane.
A relationship may be linear but not proportional and the graph does not pass through the origin.
Example 1 :
The graph shows the relationship between the weight of an object on the Moon and its weight on Earth. Explain why this relationship is proportional and also write an equation for the relationship.
Step 1 :
The graph of the given relationship contains the origin or the line is passing through the origin.
So, the relationship is proportional.
Step 2 :
Make a table relating amount earned to number of hours.
Step 3 :
Find the constant of proportionality.
Moon weight : Earth weight
1 : 6 = 1 : 6
2 : 12 = 1 : 6
3 : 18 = 1 : 6
5 : 30 = 1 : 6
The constant of proportionality is 1 : 6 or 1/6.
Step 4 :
Write an equation.
Let x represent weight on Earth.
Let y represent weight on the Moon.
The equation is y = kx
Replace k with 1/6 in the above equation.
y = (1/6)x
y = x/6
Example 2 :
The entrance fee for Mountain World theme park is $20. Visitors purchase additional $2 tickets for rides, games, and food. The equation y = 2x + 20 gives the total cost, y, to visit the park, including purchasing x tickets. Explain why the relationship between number of tickets and total cost is not proportional using a graph.
Step 1 :
Choose several values for x that make sense in context.
Step 2 :
Plot the ordered pairs from the table. Describe the shape of the graph.
Step 3 :
In the above graph, the points lie on a line. But the line does not pass through the origin. So, the relationship between number of tickets and total cost is not proportional.
After having gone through the stuff given above, we hope that the students would have understood,"Proportional and non-proportional graphs".
Apart from the stuff given above, if you want to know more about "Proportional and non proportional graphs", 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.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
Aptitude test online
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Nature of the roots of a quadratic equation worksheets
MATH FOR KIDS
Time and work word problems
Pythagorean theorem word problems
Converting repeating decimals in to fractions
L.C.M method to solve time and work problems