#### Solved Examples and Worksheet for Graphing Linear Equations

Q1Which graph represents the equation y3 = x3 + 1? A. Graph 1
B. Graph 2
C. Graph 4
D. Graph 3

Step: 1
y3 = x3 + 1
Step: 2
y = x + 3
[Multiply with 3 on both sides.]
Step: 3
Choose values for x. Step: 4
Plot the points on a graph. Step: 5
The above graph matches with the Graph 3.
Step: 6
So, Graph 3 represents the equation.
Correct Answer is :   Graph 3
Q2Which graph represents the equation y = - x + 2? A. Graph 3
B. Graph 1
C. Graph 4
D. Graph 2

Step: 1
Calculate the values of y for some values of x as shown in the following table. Step: 2
Plot the points on the graph Step: 3
So, Graph 2 represents the equation y = - x + 2.
Correct Answer is :   Graph 2
Q3Which graph represents the equation . y = - x - 3 A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
y = - x - 3
Step: 2
Choose values for x. Step: 3
Plot the points on a graph. Step: 4
The above graph matches with the graph in choice B.
Step: 5
So, choice B is the correct answer.
Correct Answer is :   Graph 2
Q4Which graph best suits the equation y = 1x? A. Graph 2
B. Graph 1
C. Graph 4
D. Graph 3

Step: 1
y = 1x
[Original equation.]
Step: 2
y = 1(- 2) = - 2
[Sustitute - 2 for x.]
Step: 3
y = 1(- 1) = - 1
[Sustitute - 1 for x.]
Step: 4
y = 1(0) = 0
[Sustitute 0 for x.]
Step: 5
y = 1(1) = 1
[Sustitute 1 for x.]
Step: 6
y = 1(2) = 2
[Sustitute 2 for x.]
Step: 7
Plot the graph for the above values of x and y. Step: 8
Among the graphs, Graph 1 suits the equation.
Correct Answer is :   Graph 1
Q5Choose the graph for the equation y = 100x. A. Graph 2
B. Graph 3
C. Graph 4
D. Graph 1

Step: 1
y = 100 x
[Original equation.]
Step: 2
At x = 0, y = 100(0) = 0
Step: 3
At x = 1, y = 100(1) = 100
Step: 4
At x = 2, y = 100(2) = 200
Step: 5
At x = 3, y = 100(3) = 300
Step: 6
Represent the above data in tabular form, as shown below. Step: 7
Among the choices, Graph 2 suits the result.
Correct Answer is :    Graph 2
Q6Which of the graphs represents the equation x = - 8? A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
The x-coordinate is always - 8, regardless of the value of y.
Step: 2
The graph of the equation x = - 8 is a vertical line 8 units to the left of the y-axis as shown in the following graph. Step: 3
The above graph matches with the graph 3.
Correct Answer is :   Graph 3
Q7Which graph represents the equation - 2x +y = 1? A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
Solve the equation for y.
- 2x +y = 1 y = 2x + 1
Step: 2
Calculate the values of y for some values of x as shown in the following table. Step: 3
Plot the points on the graph. Step: 4
So, Graph 4 represents the equation - 2x +y = 1.
Correct Answer is :   Graph 4
Q8Which graph represents the equation x + 2y = 6? A. Graph 1
B. Graph 4
C. Graph 2
D. Graph 3

Step: 1
x + 2y = 6
[Original equation.]
Step: 2
Solve the equation for y.
x + 2y = 6 y = - x2 + 3
Step: 3
Calculate the values of y for some values of x as shown in the following table. Step: 4
Plot the points and draw the line by joining them. Step: 5
Therefore Graph 4 represents the equation x + 2y = 6. .
Correct Answer is :   Graph 4
Q9Choose a graph for the equation - x- y = - 2. A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
Solve the equation for y.
- x- y = - 2 - y = x - 2
Step: 2
Choose values for x. Step: 3
Plot the points on a graph. Step: 4
The above graph matches with the Graph 2.
Correct Answer is :   Graph 2
Q10Using y-intercept and the slope, find which of the graphs represent the line y = (32)x + 1. A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
From the equation y = (32)x + 1, y-intercept is 1 and the slope is 32.
Step: 2
Plot the point (0, 1).
[Since y-intercept = 1.]
Step: 3
Move 3 units up from the point (0, 1). Then move 2 units right to plot the second point. Repeat the pattern to plot more points.
[Since slope = 32.]
Step: 4
Draw a line passing through these points. Step: 5
The above graph matches with Graph 4.
Correct Answer is :   Graph 4