Linear Equation

Definition of Linear Equation

• Linear equation is an equation of the form Ax + By = C, where A ≠ 0 and B ≠ 0. The graph of a linear equation is a straight line.

                              

Examples of Linear Equation

• The following are examples of linear equations.

5x + 7y = 1, - 13x + 6y = 0.5,
                               

Solved Example on Linear Equation

Which of the graphs represents the linear equation

x + y = 4?

Choices:

A. Graph 1

B. Graph 2

C. Graph 3

D. Graph 4

Correct Answer: B

Solution:

Step 1: x + y = 4.               [Given Equation.]

Step 2: (0) + x = 4         [To find x-intercept substitute y = 0.]

Step 3: x = 4                       [Solve for x.]

Step 4: The x-intercept is 4. So, the line crosses the x-axis at the point

(4, 0).  

Step 5: y + (0) = 4        [To find y-intercept substitute x = 0.]

Step 6: y = 4           [Solve for y.]

Step 7: The y-intercept is 4. So, the line crosses the y-axis at the point

(0, 4).   

Step 8: Plot the points (4, 0) and (0, 4) and draw a line through them.

Step 9: Among the Graphs, Graph 2 represents the graph of the linear equation x + y = 4.

Related Terms for Linear Equation

• Equation
• Straight  Line
• Graph

Additional Links for Linear Equation

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