#### Solved Examples and Worksheet for Finding Intercepts of a Linear Equation

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

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.
Q2Find the y-intercept of the line - 5x + 11y = 220.
A. 11
B. 220
C. 20
D. 511

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.]
Q3Find the y - intercept of the line 3x - 2y = 17.

A. 17
B. 15
C. - 172
D. 0
E. 173

Step: 1
3x - 2y = 17
[Original equation.]
Step: 2
3(0) - 2y = 17
[Substitute x = 0 in the equation to obtain the y - intercept.]
Step: 3
- 2y = 17
Step: 4
y = - 172
[Divide by - 2 on both sides.]
Step: 5
The y - intercept of the line is - 172.
Correct Answer is :   - 172
Q4Find the y-intercept of the equation - x + 12y = 36.
A. - 12
B. 36
C. 3
D. 0.3

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.
Q5Find the x-intercept and y-intercept of the given line: y = - 0.5x + 0.4

A. - 45, - 0.4
B. 45, 0.4
C. 54, 0.4
D. 45, - 0.4

Step: 1
y = - 0.5x + 0.4
Step: 2
To find x-intercept, put y = 0.
Step: 3
0 = - 0.5x + 0.4
Step: 4
0.5x = 0.4
Step: 5
x = 0.40.5 = 45
Step: 6
So, x-intercept is 45.
Step: 7
To find y-intercept, put x = 0.
Step: 8
y = - 0.5(0) + 0.4
Step: 9
y = 0.4
Step: 10
So, the y-intercept is 0.4.
Correct Answer is :   45, 0.4
Q6Find the y-intercept of the graph of the linear function of the data shown in the table.
 x - 4 2 4 6 y - 1 2 3 4

A. - 2
B. 1
C. 4
D. - 1

Step: 1
Slope(m) = change in y-coordinateschange in x-coordinates = 2 - (- 1)2 - (- 4) = 12
Step: 2
Equation of line of graph of the data = y - y1 = m(x - x1)
Step: 3
y + 1 = 12(x + 4)
Step: 4
2y + 2 = x + 4
Step: 5
x - 2y = - 2
Step: 6
To find the y-intercept, let x = 0.
Step: 7
0 - 2y = - 2 y = 1
[Replace x by 0.]
Step: 8
Therefore, y-intercept of the graph of the data is 1.
Q7Find the y-intercept of the graph of the linear function of the data shown in the table.
 x 3 5 7 15 y 9 13 17 33

A. 1
B. - 3
C. 3
D. 2

Step: 1
Slope(m) = change in y-coordinateschange in x-coordinates = 13 - 95 - 3 = 2
Step: 2
Equation of line of graph of the data = y - y1 = m(x - x1)
Step: 3
y - 9 = 2(x - 3)
Step: 4
2x - y = - 3
[Simplify.]
Step: 5
To find the y-intercept, let x = 0.
Step: 6
2(0) - y = -3
[Replace x by 0.]
Step: 7
y = 3.
[Divide each side by -1.]
Step: 8
Therefore, y-intercept of the graph of the data is 3.
Q8Find the x-intercept of the graph of the equation 10x - 17y = 30.

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

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.
Q9Find the y-intercept of the graph of the equation 9x - 7y = - 21.

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

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.
Q10Find the x-intercept of the line 2x - 4y = 6.
A. - 32
B. 32
C. 8
D. 3

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

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

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
Q12Find the y-intercept of the line y = 2x + 17.

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

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.
Q13Find the y-intercept of the line y = 3x + 18.

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

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.