Graph Of A Linear Relationship
Introduction to graph of a linear relationship:
Algebra is a subdivision in mathematics in which comprises of infinite number of operations on equations, polynomials, inequalities, radicals, rational numbers, logarithms, etc. Linear relationship is in which there is a proportional relation between the input and the output. Graphing linear relationship is also a part of algebra. It is similar to the graphing of ordinary equations. The co-ordinates are found first then they are plotted.
Graph of a Linear Relationship - Procedure
The following procedure has to be followed to graph linear relationship,
Step 1: Convert the given equation as y =ax+c.
Step 2: Since the given inequality is a function of x, let y =f(x).
Step 3: Therefore f(x) = ax+c.
Step 4: Substitute various values for x and find corresponding f(x).
Step 5: Table the values as follows x & f(x) the values of x as -3, -2,-1,0, 1,2,3 and for f(x) their corresponding values.
Step 6: The values in the table are the co-ordinates, graph them.
Step 7: If the inequality is given, shade the inequality region.
Example for Graphing Linear Relationship
The following are few examples for graphing linear relationship,
Problem 1:
Graph the following linear relationship, 3x +4y = 2.
Convert the given equation as
y = 1/2- 2x/3.
Since the given equation is a function of x,
Let y =f(x).
Therefore
f(x) = 1/2- 2x/3.
Substitute various values for x and find corresponding f(x).
When x= -3
f(-3) = 1/2- 2(-3)/3.
1/2 +2,
5/2, therefore the co-ordinates are (-3, 2.5)
When x= -1
f(-1) = 1/2- 2(-1)/3.
1/2 +2/3.
1.666, therefore the co-ordinates are (-1, 1.667)
When x= 0
f(0) = 1/2- 2(0)/3.
1/2
0.5, therefore the co-ordinates are (0, 0.5)
When x= 1
f(1) = 1/2- 2(1)/3.
1/2 - 2/3
-0.167, therefore the co-ordinates are (1, -0.167)
When x= 3
f(3) = 1/2- 2(3)/3
1/2 - 2
-1.5, therefore the co-ordinates are (1, -1.5)
The graph for the linear relationship is as follows,
Linear relationship graph(A)
Problem 2:
Graph the linear relationship, y = 4x.
Solution:
Let y =f(x).
Therefore
f(x) = 4x
Substitute various values for x and find corresponding f(x).
When x= -3
f(-3) = 4(-3)
12
12, therefore the co-ordinates are (-3, 12)
When x= -1
f(-1) = 4(-1)
-4
-4, therefore the co-ordinates are (-1, -4)
When x= 0
f(0) = 4(0)
0, therefore the co-ordinates are (0, 0)
When x= 1
f(1) = 4(1)
4, therefore the co-ordinates are (1, 4)
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When x= 3
f(3) =4(3)
12, therefore the co-ordinates are (1, 12)
The graph for the linear relationship is as follows,
Linear relationship graph(B)
Practice Problems:
1. Graph the linear relationship, y = 4x +9
2. Graph the linear relationship, 5y+ 4x +9 =0
3. Graph the linear relationship, 5x+ 3y=7
4. Graph the linear relationship, 2+ x+3y =0
by: Smith
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