LINEAR GRAPHS
About "Linear graphs"
Linear graphs are nothing but the graphs of straight lines. Linear relationship is being used in our day to day life. This relationship can be expressed in many different ways.
Linear graph is one way of expressing this relationship, when graphed they give a straight line. Linear graph can be sketched or plotted.
Linear graphs
An equation such as x − 2y = −2 is an example of a linear equation in the two variables x and y.
A solution of this equation is an ordered pair of numbers (x₀, y₀) so that x₀ and y₀ satisfy the equation x − 2y = −2, in the sense that x₀ − 2y₀ = −2.
Using the above method of getting all the solutions of the equation x − 2y = −2, we can plot as many points of the graph as we please to get a good idea of the graph.
For example, the adjacent picture contains the following points (given by the dots) on the graph, going from left to right:
(−5,−1.5), (−4,−1), (−2, 0), (0, 1), (2, 2), (4, 3), (6, 4).
These points strongly suggest that the graph of x − 2y = −2 is a straight line.
General equation of linear graphs
Thus, a first degree equation in two variables always represents a straight line. Hence we can take general equation of a straight line as ax + by + c = 0, with at least one of a or b not equal to zero.
For the sake of simplicity to draw lines in graphs we consider y = mx + b. as another simple form of the equation of straight line. For each value of x, the equation y = mx + b gives a value of y and we can obtain an ordered pair (x, y).
Important note
(i) If c = 0, then the equation becomes ax + b = 0 and the line passes through the origin.
(ii) If a = 0, then the equation becomes by + c = 0 and the line is parallel to x-axis.
(iii) If b = 0, then the equation becomes ax + c = 0 and the line is parallel to y-axis.
Procedure to draw a Linear Graph
When graphing an equation, we usually begin by creating a table of x and y values. We do this by choosing three x values and computing the corresponding y values.
Although two points are sufficient to sketch the graph of a line, we usually choose three points so that we can check our work.
Step 1 :
Using the given equation construct a table of with x and y values.
Step 2 :
Draw x-axis and y-axis on the graph paper.
Step 3 :
Select a suitable scale on the coordinate axes.
Step 4 :
Plot the points
Step 5 :
Join the points and extend it to get the line.
Drawing linear graph - Example
Draw the graph of the line joining the points
(3, 5) and (-5, 1)
Solution :
Step 1 :
Draw the x-axis and y-axis on a graph sheet with 1 cm = 1 unit on both axes.
Step 2 :
We plot the two given points (3, 5), (-5, 1) on the graph sheet.
Step 3 :
We join the points by a line segment and extend it on either direction.
Step 4 :
We get the required linear graph.
After having gone through the stuff given above, we hope that the students would have understood "Graphs of linear equations".
Apart from the stuff given above, if you want to know more about "Linear graphs", please click here
Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
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
Trigonometry 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
Recent Articles
-
Integration Problems Worksheet
Mar 03, 21 07:44 AM
Integration Problems Worksheet
-
Integrating Trigonometric Functions
Mar 03, 21 06:39 AM
Integrating Trigonometric Functions
-
Practice Questions on Integration
Mar 03, 21 06:19 AM
Practice Questions on Integration
