Download Name - Spring Branch ISD

Name _______________________
Review for Test - KEY
(slope-intercept form, point-slope form, standard form, parallel lines,
perpendicular lines, solving systems of equations using graphing,
substitution, and elimination)
1. How can you write an equation of a line in slope-intercept form when you are
given the graph of the line?
Pick out two points on the line. Use rise over run to determine the slope
of the line. Look at where the line crosses the y-axis. Plug the slope and yintercept in the slope-intercept form (y = mx + b).
2. What is the first step when writing an equation of a line in slope-intercept form
when you are given two points on the line?
You must first find the slope of the line.
m
y 2  y1
x 2  x1
3. What do we know if two lines are parallel?
The two lines have the same slope.
4. What do we know if two lines are perpendicular?
The two lines have slopes that are opposite signs and reciprocals of each
other.
Write this equation in slope-intercept form.
5. -6x – 2y = 8
-2y = 6x + 8
y = -3x - 4
Write this equation in standard form.
2
6. y = x – 5
3
3(y =
2
x – 5)
3
3y = 2x – 15
-2x + 3y = - 15
There are other possible answers to this, such as:
2x – 3y = 15
-4x + 6y = -30
4x – 6y = 30
For problems 7 & 8, write an equation, make a graph, find the slope and tell what
it means for the situation, and find the intercepts and tell what they mean for
the situation. Label and circle each part.
7. An abandoned bank account has a balance of $412 and the bank charges a $4 a
month fee for the account.
y = 412 – 4x
m = -4
The slope represents the amount of money the bank charges each month.
x-intercept = 103 OR (103, 0)
y-intercept = 412 OR (0, 412)
The x-intercept represents how many months it would take for the balance in
the account to equal zero.
The y-intercept represents the amount of money in the account initially.
8. An employee earns $8 per hour.
y = 8x
m=8
The slope represents the amount of money the employee makes each hour.
x-intercept = 0 OR (0,0)
y-intercept = 0 OR (0,0)
The x-intercept represents how many hours the employee has worked when
they have earned no money.
The y-intercept represents how much money the employee has earned when
they have worked zero hours.
Use point-slope form to solve this problem. Then, write the equation of the line in
slope-intercept form.
1
9. m =  ; (5, -7)
5
1
y – (-7) =  (x – 5)
5
1
y+7=  x+1
5
1
y=  x-6
5
Use slope-intercept to solve this problem. Then, write the equation of the line in
slope-intercept form.
3
10. slope =
and goes through the point (-2, -11)
2
-11 =
3
(-2) + b
2
-11 = -3 + b
b = -8
y=
3
x-8
2
Write the equation of the line in slope-intercept form that goes through these two
points. You may solve it however you want to, though.
11. (-1, -6) and (-5, -9)
m
6  (9)
1  (5)

y = mx + b
3
-6 = (-1) + b
4
3
-6 = - + b
4
1
b = -5
4
3
1
y= x–5
4
4
6  9
1  5

3
4
OR
y – y1= m(x – x1)
3
y – (-6) = (x – (-1))
4
3
y+6=
(x + 1)
4
3
3
y+6= x+
4
4
3
1
y= x-5
4
4
Identify which lines are parallel.
5
3
12. y = x + 2; 6y + 3 = -10x; 5x – 3y = 15; y =  x - 5
3
5
y=
1
5
5
3
x + 2; y = - x - ; y = x – 5; y =  - 5
3
3
3
5
2
5
5
The first and third lines are parallel because their slope = .
3
13. Write an equation in slope-intercept form for the line that passes through (6, -2)
and is perpendicular to y = -3x + 2.
1
m=
3
1
-2 =
(6) + b
OR
y – (-2) =
3
1
(x – 6)
3
-2 = 2 + b
y+2=
1
x-2
3
b = -4
y=
1
x-4
3
y=
1
x-4
3
14. Write an equation that describes the graph shown below.
40
(0, 15), (3, 22), (6, 29),
(9, 36)
amount earned ($)
35
30
25
m
20
15
y=
10
22  15
30
7
3
5
0
0
1
2
3
4
5
6
7
time (hours)
15. Graph this line: y = -
3
x -1
5
The line crosses the y-axis at -1. From
there the line goes up and to the left (a
negative slope). From the y-intercept you
should go up 3 and to the left 5 (and arrive at
(-5, 2)) or go down 3 and to the right 5 (and
arrive at (5, -4)).
8
9
10

x + 15
7
3
16. At age twelve Patrick weighed 43 kg and at 14 he weighed 50 kg. Find a linear
equation relating Patrick’s weight w to his age a.
(12, 43) and (14, 50)
m
50  43
14  12
43 =
7

7
2
(12) + b
OR
y – 43 =
2
43 = 42 + b
y – 43 =
7
2
7
(x – 12)
x - 42
2
b=1
y=
7
x+1
2
y=
7
x+1
2
7
w= a+1
2
17. Each month 50 new people come to live in Centertown. After 3 months, the
town has 25,500 people. Write an equation relating the number of months m to the
number of people n in the town.
m = 50; (3, 25,500)
25,500 = 50(3) + b
25,500 = 150 + b
b = 25,350
y = 50x + 25,350
OR
n = 50m + 25,350
Solve this system by graphing.
18. y = 4
y=x-3
The first equation is a horizontal line that
crosses the y-axis at 4 (y = ____ lines are
horizontal and x = ___ lines are vertical).
The second equation crosses the y-axis at -3.
The slope is 1. So, from the y-intercept go up 1
and to the right 1 (to arrive at (1, -2).
These two lines cross at (7, 4).
y – 25,500 = 50(x – 3)
y – 25,500 = 50x - 150
y = 50x + 25,350
Solve this system by substitution.
19. y = x - 3
-4x - 2y = 12
-4x – 2(x – 3) = 12
-4x – 2x + 6 = 12
-6x + 6 = 12
-6x = 6
x = -1
y=x-3
y = -1 - 3
y = -4
(-1, -4)
Solve this system by elimination (linear combination).
20. 5x + 3y = -6
3x + 4y = 3
3(5x + 3y = -6)
5(3x + 4y = 3)
15x + 9y = -18
15x + 20y = 15
Subtract to get:
-11y = -33
y=3
5x + 3(3) = -6
5x + 9 = -6
5x = -15
x = -3
(-3, 3)
Solve these systems by whichever method you want to.
21. y + 4x – 3 = 0
8x + 2y = 6
y = -4x + 3
8x + 2(-4x + 3) = 6
8x – 8x + 6 = 6
0+6=6
6=6
These two equations are the same line so the solution is all points on the
line. You can prove to yourself that they are the same line by changing both of
them to slope-intercept form.
22. 2x - 3y = 2
7x - 5y = -4
5(2x – 3y = 2)
-3(7x – 5y = -4)
10x – 15y = 10
-21x + 15y = 12
Add to get:
-11x = 22
x = -2
2(-2) – 3y = 2
-4 – 3y = 2
-3y = 6
y = -2
(-2, -2)
23. y – x = -7
-4x + 2y = -8
y=x-7
-4x + 2(x – 7) = -8
-4x + 2x – 14 = -8
-2x – 14 = -8
-2x = 6
x = -3
y = -3 - 7
y = -10
(-3, -10)
24. 3x - 2y = 14
x – 4y = 8
x = 4y + 8
3(4y + 8) – 2y = 14
12y + 24 – 2y = 14
10y + 24 = 14
10y = -10
y = -1
x = 4(-1) + 8
x = -4 + 8
x=4
(4, -1)
25. -9x + y = 6
1
x= y
3
1
-9( y) + y = 6
3
-3y + y = 6
-2y = 6
y = -3
1
(-3)
3
x = -1
x=
(-1, -3)
You must use systems of equations to solve these word problems.
26. The sum of two numbers is seven. Twice the smaller number subtracted from
three times the larger number is eleven. Find the two numbers.
x+y=7
3y - 2x = 11
x = smaller #
y = larger #
x = -y + 7
3y – 2(-y + 7) = 11
3y + 2y – 14 = 11
5y – 14 = 11
5y = 25
y=5
x+5=7
x=2
The smaller number is 2 and the larger number is 5.
27. The length of a rectangle is 3 more than its width. The perimeter of the
rectangle is 58 cm. What are the rectangle’s dimensions?
l=3+w
2l + 2w = 58
2(3 + w) + 2w = 58
6 + 2w + 2w = 58
4w + 6 = 58
4w = 52
w = 13
l = 3 + 13
l = 16
The length is 16 cm and the width is 13 cm.
28. Dustin is remodeling his house. He bought 3 sinks and 3 toilets for $600. He
returned 1 toilet and bought 2 more sinks for $25. How much would 4 sinks and 2
toilets cost?
3x + 3y = 600
2x – 1y = 25
x = cost of sink
y = cost of toilet
3x + 3y = 600
3(2x – 1y = 25)
3x + 3y = 600
6x – 3y = 75
Add to get:
9x = 675
x = 75
2(75) – 1y = 25
150 – 1y = 25
-1y = -125
y = 125
Sinks cost $75 and toilets cost $125.
The 4 sinks and 2 toilets cost $550.
29. Marcia has $84 less than three times as much as Sue. Together they have $132.
How much money does each girl have?
x = 3y – 84
x + y = 132
3y – 84 + y = 132
4y – 84 = 132
4y = 216
y = 54
x + 54 = 132
x = 78
Marcia has $78 and Sue has $54.
x = amount of $ Marcia has
y = amount of $ Sue has