Graphing Linear Equations

Graphing Linear Equations is one of the most important concepts of algebra and proper understanding is necessary to be good with it. Get help from an algebra tutor online and learn about graphing linear equations, understand all the basic and advance concepts of equations and achieve quality help here. Below is an example of graphing linear equations with one variable for a better understanding:

Example : ax + b = 0 is a linear equation in one variable.

To represent a graph of linear equation in one variable ,

Consider the equation 2x + 4 = 0

2x = -4

x = $\frac{-4}{2}$

x = -2

Since this equation is independent of y, for all values of y, x = -2

Hence x = -2 is a line parallel to the y-axis at x = -2.

Before learning on how to graph linear equations in one variable x = -2, let us understand the basics on how to graph linear equations.

How to graph linear equations Of y = mx + c

Step1: Choose the convenient values of x and find the corresponding values of y

Step 2: Prepare a table for different pairs of values of x and y

Step 3: Draw the axes on a graph paper and chose a suitable sale.

Step 4: Plot the ordered pairs fro the above table on the graph paper

Step 5: Join these points by a straight line This straight line is the graph of y = mx + c

Remark : In the equation y = mx + c, we say that

(i) m is the slope of the line

(ii) c is the y = intercept of the line.

Example : How to Graph Linear Equations of the line y = 2x + 3. Write down its

(i) y-intercept

(ii) slope.

Solution : We have x = 1

→ y = (2 x 1 = 3) = 5 x = - 2

→ y = {2 x (-2) + 3} = - 1

Thus, we have the following table

x	1	- 2
y	5	- 1

Plot the Points A(1, 5) and B( - 2, - 1) on a graph paper.

Join AB and produce it. Then, AB is the required graph of the line y = 2x + 3 clearly,

(i) y-intercept = 3

(ii) slope = 2

Consider the equation y - 5 = 0

y - 5 = 0

y = 5

Since this equation is independent of x, for all values of x, y = 5.

Hence the graph of y = 5 is a line parallel to the x-axis at y = 5.

Question : Plot the graph of 4x+y=4

Suggested Answer :

x = $\frac{4 - y}{4}$

Put y = -4,

x = $\frac{4 - (- 4)}{4}$ = $\frac{4 + 4}{4}$

= $\frac{8}{4}$

x = 2

Put y = 8,

x = $\frac{4 - (8)}{4}$ = $\frac{-4}{4}$

x = -1

Put y = -8,

x = $\frac{4 -(-8)}{4}$ = $\frac{4 + 8}{4}$

x = $\frac{12}{4}$

x = 3

Students can also learn about the drawing graphs for linear equations with 2 variables and compare these examples with them to understand the differences between them better.