Name _________________________________________
Date ___________________
Algebra – Pd ___
Systems of Equs, Parallel & Perpendicular Lines (Chap 5)
Review Sheet
Part 1: Write the appropriate number choice in the space provided.
_____ 1) Which point is located on the line represented by the equation 𝑦 + 4 = −5(𝑥 − 3)?
[1] (−4, −5)
[2] (−5, −4)
[3] (3, −4)
[4] ( −3,4)
5
_____ 2) What is 𝑦 = − 3 𝑥 − 6 written in standard form using integers?
[1]
5
3
𝑥 + 𝑦 = −6
[2] 5𝑥 + 3𝑦 = −6
[3] 5𝑥 + 3𝑦 = −18 [4] −5𝑥 + 3𝑦 = 6
_____ 3) Which interval notation represents the set of all numbers from 3 through 6 inclusive?
[1] (3,6)
[2] (3,6]
[3] [3,6)
[4] [3,6]
_____4) Which equation is equivalent to 𝑦 − 6 = −12(𝑥 + 4)?
[1] 𝑦 = −6𝑥 − 48 [2] 𝑦 = 6𝑥 − 48
[3] 𝑦 = −12𝑥 − 42 [4] 𝑦 = −12𝑥 − 54
_____ 5) Which equation represents a line that passes through the points (6, −3) and (−4, −9)?
3
5
[1] 𝑦 + 4 = − 5 (𝑥 + 9)
[2] 𝑦 + 4 = 3 (𝑥 + 9)
3
[3] 𝑦 − 3 = 5 (𝑥 + 6)
_____ 6) Solve the equation for x: ax + y = c
𝑐−𝑦
𝑐−𝑦
[1] 𝑎
[2] 𝑥
3
[4] 𝑦 + 3 = 5 (𝑥 − 6)
[3]
𝑐+𝑦
𝑎
[4]
𝑦−𝑐
𝑎
_____ 7) Which equation would be parallel to y = 5 and cross through the point (-2, -6)?
(1) x = -2
(2) x = -6
(3) y = -2
(4) y = -6
_____ 8) State the solution of the system of equations graphed below.
(1) (0,3)
(2) (3, −1)
(3) (−1, 3)
(4) (1, 3)
_____ 9) If a system of equations has no solution, what does the graph look like?
(1) intersecting lines
(2)parallel lines
(3) skew lines
(4) same line
Part 2: Solve the following system graphically in your notebooks, then check. No Work = No Credit!
3
10) 𝑦 + 4𝑥 = −1
11) 𝑦 − 2 = 5 (𝑥 − 10)
12) 𝑦 = −4
𝑦 = 2𝑥 − 7
𝑦 + 11 = 2(𝑥 + 7)
9𝑥 – 18𝑦 = 126
Part 3: Use the given information to solve for slope-intercept form and graph both lines.
13) Find the equation of the line parallel to 𝑦 + 3𝑥 = 3𝑥 + 8 and passing through the point (5,2).
1
14) What is the equation of the line perpendicular to 𝑦 = 2 𝑥 + 4 and passes through (2, 5)?
15) Find the equation of the line perpendicular to 3𝑥 + 9𝑦 = 54 and passing through (3, 5).
16) What is the equation of the line parallel to 𝑦 − 4 = −2(3𝑥 − 4) and passes through (1, −6)?
1
17)Find the equation of the line perpendicular to 𝑦 + 12 = 2 (4𝑥 + 12) and passes through (2, −2)
18) Find the equation of the line parallel to 2𝑥 − 4𝑦 = −36 and passing through (−2, 3)
19) Find the equation of the line parallel to 𝑥 = 3 and passing through (−2, 6)
20) Find the equation of the line perpendicular to 2𝑥 − 3𝑦 = 21 and passing through (6, −3).
ANSWER KEY:
Part 1:
1) (3)
7) (4)
2) (3)
8) (4)
3) (4)
9) (2)
4) (3)
5) (4)
6) (1)
Part 2:
10) 𝑦 = −4𝑥 − 1
3
11) 𝑦 = 5 𝑥 − 4
𝑦 = 2𝑥 − 7
(1, −5)
12) 𝑦 = −4
1
𝑦 = 2𝑥 + 3
(−5, −7)
𝑦 = 2𝑥 − 7
(6, −4)
Part 3:
Given:
13) 𝑦 = 8
Parallel/ Perp.:
𝑦=2
Given:
1
14) 𝑦 = 2 𝑥 + 4
15) 𝑦 = − 𝑥 + 6
𝑦 = 3𝑥 − 4
16) 𝑦 = −6𝑥 + 12
17) 𝑦 = 2𝑥 − 6
𝑦 = −2𝑥 − 1
18) 𝑦 = 𝑥 + 9
19) 𝑥 = 3
𝑥 = −2
20) 𝑦 = 𝑥 − 7
1
3
1
1
2
2
3
Parallel/ Perp.:
𝑦 = −2𝑥 + 9
𝑦 = −6𝑥
1
𝑦 = 2𝑥 + 4
3
𝑦 = −2𝑥 + 6
Name _____________________________________________
Algebra I – Pd ___
Systems
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11)
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Date ____________________
Q1 Test 2 – Review
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Extra