Solved Examples and Worksheet for Finding Intercepts of Linear Relations

Q1Find the x-intercept of the line x + y = 4.
A. 3
B. 5
C. 4
D. 6

Solutions
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Step: 1
x + y = 4
  [Given equation.]
Step: 2
x + (0) = 4
  [To find x-intercept substitute y = 0.]
Step: 3
x = 4
  [Solve for x.]
Step: 4
The x-intercept of the line is 4.
Correct Answer is :   4
Q2Find the y-intercept of the line - 5x + 11y = 220.
A. 11
B. 220
C. 20
D. 511

Solutions
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Step: 1
- 5x + 11y = 220
  [Given Equation.]
Step: 2
- 5(0) + 11y = 220
  [To find y intercept substitute x = 0.]
Step: 3
y = 20
  [Solve for y.]
Correct Answer is :   20
Q3Find the x-intercept of the graph of the equation 7x - 5y = 21.

A. 3
B. 21
C. 5
D. 0

Solutions
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Step: 1
To find the x-intercept, substitute y = 0 in the equation.
Step: 2
7x - 5y = 21
  [Write original equation.]
Step: 3
7x - 5(0) = 21
  [Replace y with 0.]
Step: 4
7x = 21
  [Solve for x.]
Step: 5
x = 3
Step: 6
The x-intercept is 3.
Correct Answer is :   3
Q4Find the y-intercept of the graph of the equation 3x - 5y = - 25.
A. 165
B. 5
C. - 165
D. - 4

Solutions
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Step: 1
To find the y-intercept, substitute x = 0 in the equation.
Step: 2
3x - 5y = - 25
  [Write original equation.]
Step: 3
3(0) - 5y = - 25
  [Replace x with 0.]
Step: 4
- 5y = - 25
  [Solve for y.]
Step: 5
y = 5
Step: 6
The y-intercept is 5.
Correct Answer is :   5
Q5Find the y-intercept of the equation - x + 12y = 36.
A. - 12
B. 36
C. 3
D. 0.3

Solutions
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Step: 1
To find the y-intercept, sustitute x = 0 in the equation.
Step: 2
- x + 12y = 36
  [Write original equation.]
Step: 3
- (0) + 12y = 36
  [Replace x with 0.]
Step: 4
12y = 36
  [Solve for y.]
Step: 5
y = 3
Step: 6
The y-intercept is 3.
Correct Answer is :   3
Q6What are the x- and y-intercepts of the line shown in the graph?

A. x-intercept is 0 and y-intercept is 0
B. x-intercept is 4 and y-intercept is 0
C. x-intercept is 4 and y-intercept is 4
D. x-intercept is 0 and y-intercept is 4

Solutions
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Step: 1
The x-intercept is the x-coordinate of the point where a line crosses the x-axis.
Step: 2
In the figure shown, the line crosses the x-axis at x = 4.
Step: 3
So, the x-intercept of the line is 4.
Step: 4
The y-intercept is the y-coordinate of the point where a line crosses the y-axis.
Step: 5
In the figure shown, the line crosses the y-axis at y = 4.
Step: 6
So, the y-intercept of the line is 4.
Step: 7
The x- and y- intercepts of the line are 4 and 4 respectively.
Correct Answer is :   x-intercept is 4 and y-intercept is 4
Q7Find the x-intercept of the graph of the equation x + 3y = - 14.

A. - 14
B. - 14 - 3y
C. - 3
D. - 13

Solutions
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Step: 1
To find the x-intercept, substitute y = 0 in the equation.
Step: 2
x + 3y = - 14
  [Write original equation.]
Step: 3
x + 3(0) = - 14
  [Replace y with 0.]
Step: 4
x = - 14
  [Solve for x.]
Step: 5
The x-intercept is - 14.
Correct Answer is :   - 14
Q8Find the x-intercept of the graph of the equation 10x - 17y = 30.

A. 10
B. 1017
C. - 3017
D. 3

Solutions
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Step: 1
To find the x-intercept, substitute y = 0 in the equation.
Step: 2
10x - 17y = 30
  [Write original equation.]
Step: 3
10x - 17(0) = 30
  [Replace y with 0.]
Step: 4
10x = 30
  [Solve for x.]
Step: 5
x = 3
Step: 6
The x-intercept is 3.
Correct Answer is :   3
Q9Find the y-intercept of the graph of the equation 9x - 7y = - 21.

A. 3
B. - 21
C. - 7
D. - 73

Solutions
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Step: 1
To find the y-intercept, substitute x = 0 in the equation.
Step: 2
9x - 7y = - 21
  [Write original equation.]
Step: 3
9(0) - 7y = - 21
  [Replace x with 0.]
Step: 4
- 7y = - 21
  [Solve for y.]
Step: 5
y = 3
Step: 6
The y-intercept is 3.
Correct Answer is :   3
Q10Find the y-intercept of the line 4x - 3y = 27.

A. 274
B. - 30
C. 24
D. - 9

Solutions
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Step: 1
To find the y-intercept, substitute x = 0 in the equation.
Step: 2
4x - 3y = 27
  [Write original equation.]
Step: 3
4(0) - 3y = 27
  [Replace x with 0.]
Step: 4
- 3y = 27
  [Solve for y.]
Step: 5
y = - 9
Step: 6
The y-intercept is - 9.
Correct Answer is :   - 9
Q11Find the y-intercept of the line y = 2x + 17.

A. 2
B. - 17
C. - 172
D. 17

Solutions
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Step: 1
To find the point on the y-axis intercepted by the equation, substitute x = 0.
Step: 2
y = 2x + 17
  [Write original equation.]
Step: 3
y = 2(0) + 17
  [Replace x with 0.]
Step: 4
y = 17
  [Solve for y.]
Step: 5
The y-intercept = 17.
Correct Answer is :   17
Q12Find the y-intercept of the line y = 3x + 18.

A. - 9
B. 18
C. 9
D. - 18

Solutions
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Step: 1
To find the point on the y-axis intercepted by the equation, substitute x = 0.
Step: 2
y = 3x + 18
  [Write original equation.]
Step: 3
y = 3(0) + 18
  [Replace x with 0.]
Step: 4
y = 18
  [Solve for y.]
Step: 5
The y-intercept = 18.
Correct Answer is :   18
Q13Find the y-intercept of the graph of the equation 3x - 5y = - 30.

A. - 4
B. 6
C. - 165
D. 165

Solutions
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Step: 1
To find the y-intercept, substitute x = 0 in the equation.
Step: 2
3x - 5y = - 30
  [Write original equation.]
Step: 3
3(0) - 5y = - 30
  [Replace x with 0.]
Step: 4
- 5y = - 30
  [Solve for y.]
Step: 5
y = 6
Step: 6
The y-intercept is 6.
Correct Answer is :   6

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