Homework 5 - Section 3.3 #5
Intermediate Algebra / MAT 135 Fall 2016 possible master (Prof. Fleischner)
Student Name/ID:
1. Rewrite the equation in A x + B y = C form.
Use integers for A, B, and C.
y + 5 = −3 x + 4
2. Rewrite the equation in A x + B y = C form.
Use integers for A, B, and C.
y−4=5 x+2
3. Find the slope and the y-intercept of the line.
−6x + 3y = −3
Write your answers in simplest form.
4. Find the slope and the y-intercept of the line.
−3x − 4y = −20
Write your answers in simplest form.
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5. The equation of a line is given below.
3x + 2y = −6
Find the slope and the y-intercept.
Then use them to graph the line.
slope: _______________
y-intercept: _______________
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
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6. The equation of a line is given below.
−3x − 5y = −15
Find the slope and the y-intercept.
Then use them to graph the line.
slope: _______________
y-intercept: _______________
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
7.
A line passes through the point −4, 3 and has a slope of −
5
.
4
Write an equation in slope-intercept form for this line.
8.
A line passes through the point 10, 3 and has a slope of
3
.
2
Write an equation in slope-intercept form for this line.
5
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9.
A line passes through the point 4, −3 and has a slope of −
5
.
4
Write an equation in point-slope form for this line.
10.
A line passes through the point −4, 2 and has a slope of
3
.
2
Write an equation in point-slope form for this line.
11. Write an equation of the line below.
8
7
6
5
4
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
y
x
1 2 3 4 5 6 7 8
12. Write an equation of the line below.
8
7
6
5
4
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
y
x
1 2 3 4 5 6 7 8
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13. Find an equation for the line below.
y
8
6
4
2
x
-8
-6
-4
-2
2
4
6
8
-2
-4
-6
-8
14. Find an equation for the line below.
y
8
6
4
2
x
-8
-6
-4
-2
2
4
6
8
-2
-4
-6
-8
ALEKS Homework 5 - Section 3.3 #5 - 04/30/2016 12:42 PM EDT - Copyright © 2016 UC Regents and ALEKS Corporation.
8, −6
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15. Write equations for the horizontal and vertical lines passing through the point 8, −6 .
horizontal line:
vertical line:
16. Write equations for the horizontal and vertical lines passing through the point 3, 7 .
horizontal line:
vertical line:
17. Consider the line 8x + 3y = −4.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
18. Consider the line −9x − 6y = −4.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
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19. The equations of three lines are given below.
Line 1: 3y = 5x + 2
Line 2: 6x − 10y = −8
Line 3: y =
5
x+7
3
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2:
Parallel
Perpendicular
Neither
Line 1 and Line 3:
Parallel
Perpendicular
Neither
Line 2 and Line 3:
Parallel
Perpendicular
Neither
20. The equations of three lines are given below.
Line 1: 2y = −3x + 5
Line 2: y = −
3
x−3
2
Line 3: 4x − 6y = −6
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2:
Parallel
Perpendicular
Neither
Line 1 and Line 3:
Parallel
Perpendicular
Neither
Line 2 and Line 3:
Parallel
Perpendicular
Neither
y = 7x − 1
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21. Consider the line y = 7x − 1.
(a) Find the equation of the line that is perpendicular to this line and passes through the point
−3, 2 .
(b) Find the equation of the line that is parallel to this line and passes through the point −3, 2 .
22.
Consider the line y =
3
x − 0.
2
(a) Find the equation of the line that is parallel to this line and passes through the point 9, 6 .
(b) Find the equation of the line that is perpendicular to this line and passes through the point
9, 6 .
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Homework 5 - Section 3.3 #5 Answers for class Intermediate
Algebra / MAT 135 Fall 2016 possible master
1. 3x + y = −17
2. −5x + y = 14
3. slope: 2
y-intercept: −1
3
4
y-intercept: 5
4.
slope: −
3
2
y-intercept: −3
5.
slope: −
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
3
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3
5
y-intercept: 3
6.
slope: −
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
7.
8.
9.
y=−
y=
5
x−2
4
3
x − 12
2
y+3= −
10.
11.
y−2=
y=−
5
x−4
4
3
x+4
2
1
x−1
3
12. y = −2x + 3
13.
y=−
3
4
22
x−
7
7
27
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14.
y=
3
27
x+
5
5
15. horizontal line: y = −6
vertical line: x = 8
16. horizontal line: y = 7
vertical line: x = 3
17.
18.
Slope of a parallel line:
−
Slope of a perpendicular line:
3
8
Slope of a perpendicular line:
2
3
Slope of a parallel line:
−
8
3
3
2
19.
Line 1 and Line 2:
Parallel
Perpendicular
Neither
Line 1 and Line 3:
Parallel
Perpendicular
Neither
Line 2 and Line 3:
Parallel
Perpendicular
Neither
20.
Line 1 and Line 2:
Parallel
Perpendicular
Neither
Line 1 and Line 3:
Parallel
Perpendicular
Neither
Line 2 and Line 3:
Parallel
Perpendicular
Neither
21.
Equation of perpendicular line: y = −
Equation of parallel line:
1
11
x+
7
7
y = 7x + 23
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22.
Equation of parallel line:
y=
3
15
x−
2
2
Equation of perpendicular line: y = −
2
x + 12
3
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