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

Q1Choose a graph for the equation - y = x - 2. A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
Choose values for x. Step: 2
Plot the points on a graph. Step: 3
The above graph matches with the Graph 2.
Step: 4
So, Graph 2 is the correct answer.
Correct Answer is :   Graph 2
Q2Which graph represents the equation y = - 3x + 1? A. Graph 1
B. Graph 3
C. Graph 2
D. Graph 4

Step: 1
y = - 3x + 1
[Write the equation in slope- intercept form.]
Step: 2
The slope is - 3 and y-intercept is 1.
[m = - 3, b = 1.]
Step: 3
Plot the point (0, b) when b is 1.
Step: 4
Use the slope to locate a second point on line.
Step: 5
m = - 31 = riserun move 3 units downmove 1 unit right
Step: 6
Draw a line through the two points. Step: 7
Graph of the equation y = - 3x + 1 matches with Graph 2.
Correct Answer is :   Graph 2
Q3Identify the graph of the equation x - 3y = - 6. A. Graph 2
B. Graph 1
C. Graph 3
D. Graph 4

Step: 1
x - 3y = - 6 y = x3 + 2
[Write the equation in slope-intercept form.]
Step: 2
The slope is 13 and y-intercept is 2.
Step: 3
Plot the point (0, 2).
Step: 4
From (0, 2), move 1 unit up and 3 units right. You get another point (3, 3).
Step: 5
Draw a line through these two points. Step: 6
Graph of the equation x - 3y = - 6 matches with Graph 2.
Correct Answer is :   Graph 2
Q4Which graph represents the equation x = - 2? A. Graph 3
B. Graph 1
C. Graph 4
D. Graph 2

Step: 1
The x-coordinate is always - 2, regardless of the value of y.
Step: 2
The graph of the equation x = - 2 is a vertical line 2 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
Q5Which graph represents the equation y = 13x - 1? A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
y = 13x - 1
Step: 2
Choose values for x:
Step: 3
When x = 0, y = 13(0) - 1 = - 1
[Substitute x = 0 in equation.]
Step: 4
When x = 3, y = 13(3) - 1 = 0
[Substitute x = 3 in equation.]
Step: 5
When x = - 3, y = 13(- 3) - 1 = - 2
[Substitute x = - 3 in equation.]
Step: 6
The points are, (0, - 1), (3, 0), and (- 3, - 2).
Step: 7
Draw a line passing through these points. Step: 8
The above graph matches with Graph 2.
Correct Answer is :   Graph 2
Q6Choose a graph for the equation y = 2x - 3 A. Graph 3
B. Graph 4
C. Graph 2
D. Graph 1

Step: 1
Calculate the values of y for certain values of x as shown in the following table. Step: 2
Plot the points on the graph. Step: 3
Therefore, Graph 1 represents the equation y=2x-3.
Correct Answer is :   Graph 1
Q7Which of the graphs represents the equation y2 = x3 - 1 A. Graph 3
B. Graph 1
C. Graph 2
D. Graph 4

Step: 1
y2 = x3 - 1 ⇒ y = 23x - 2
[Multiply by 2 on both sides of the equation.]
Step: 2
When x = 0, y = 23 (0) - 2 = - 2
[Substitute x = 0 in the equation.]
Step: 3
When x = 3, y = 23(3) - 2 = 0
[Substitute x = 3 in the equation.]
Step: 4
Thus, the points (0, -2) and (3, 0) are the solutions of the equation y2 = x3 - 1.
Step: 5
Draw a line passing through these points. Step: 6
Therefore, graph 1, represents the equation y2 = x3 - 1.
Correct Answer is :   Graph 1
Q8Which of the graphs represents the equation y = - 34x + 3? A. Graph 3
B. Graph 4
C. Graph 1
D. Graph 2

Step: 1
y = - 34x + 3
Step: 2
When x = 0, y = - 34 (0) + 3 = 3
[Substitute x = 0 in the equation.]
Step: 3
When x = 4, y = - 34(4) + 3 = 0
[Substitute x = 4 in the equation..]
Step: 4
Thus, the points (0, 3) and (4, 0) are the solutions of the equation y = - 34 x + 3.
Step: 5
Draw a line passing through these points. Step: 6
Therefore, graph 1 represents the equation y = - 34x + 3.
Correct Answer is :   Graph 1
Q9Which of the graphs represents the equation y = - 12x? A. Graph 1
B. Graph 3
C. Graph 4
D. Graph 2

Step: 1
y = - 12x
Step: 2
When x = 2, y = - 12 (2) = - 1
[Substitute x = 2 in the equation.]
Step: 3
When x = - 2, y = - 12( - 2) = 1
[Substitute x = - 2 in the equation.]
Step: 4
Thus, the points (2, - 1) and ( - 2, 1) are the solutions of the equation y = - 12x.
Step: 5
Draw a line passing through these points. Step: 6
Therefore, graph 2 represents the equation y = - 12x
Correct Answer is :   Graph 2
Q10Which of the graphs represents the equation y = 43x - 1? A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
y = 43x - 1
Step: 2
When x = 3, y = 43(3) - 1 = 3
[Substitute x = 3 in the equation.]
Step: 3
When x = 0, y = 43(0) - 1 = - 1
[Substitute x = 0 in the equation.]
Step: 4
Thus, the points (0, - 1) and (3, 3) are the solution of the equation y = 43x - 1.
Step: 5
Draw a line passing through these points. Step: 6
Therefore, graph 4, represents the equation y = 43x - 1.
Correct Answer is :   Graph 4
Q11Which of the graphs represents the equation y = - 45 ? A. Graph 4
B. Graph 2
C. Graph 3
D. Graph 1

Step: 1
y = - 45 = - 0.8
[Simplify the equation.]
Step: 2
The y - coordinate is always - 0.8, regardless of the value of x.
Step: 3
Thus, the graph of the equation y = - 0.8 is a horizontal line which is 0.8 units below the x-axis as shown in the graph. Step: 4
Therefore, graph 2 represents the equation y = - 45
Correct Answer is :   Graph 2