Olympic College Math 94 – Test on Topics 6, to 8
Math 94 – Test on Topics 6 to 8
1.
Plot each point: A(2,4), B(– 2, –4), C(0, – 4)
y
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
-3
-4
-5
2. Find the missing value of x that makes (x, – 6) a solution to the equation:
y = 2x – 8
3. (a) Determine which of the three ordered pairs does not satisfy the given equation.
Equation: 2x – 3y = 9
Points: (3,-2.5) (0, – 3) (– 3, – 5)
(b) Plot the points that satisfy the equation and draw a straight line through the points:
y
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
-3
-4
-5
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Olympic College Math 94 – Test on Topics 6, to 8
y
4. Graph the line y = – 3
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
-3
-4
-5
5. Graph the line 2x – 3y = 12, using the x-intercepts and y-intercepts:
y
5
4
3
2
1
x
-5 -4 -3 -2 -1 0
-1
1
2
3
4
5
-2
-3
-4
-5
6. (a) By calculating the rise and the run find the slope of this line..
y
5
4
3
(b) What are the coordinates of the y-intercept?
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
(c) Write down the equation of this line.
-3
-4
-5
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Olympic College Math 94 – Test on Topics 6, to 8
7.
8.
For computer repairs, a technician charges a flat fee of $25.50, plus $20 per hour required for the
repair.
(a)
Write an equation for the cost, C, she charges in terms of hours required, h.
(b)
How much will it cost for a 3 hour repair?
(c)
If you get $225.50 bill how many hour did the technician work for?
Find the slope of the line through the points
(a) (– 5, – 1) and (10,6)
(b) (3, – 3) and (– 3 , – 3)
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Olympic College Math 94 – Test on Topics 6, to 8
9. What is the slope and the coordinates of the y-intercept for each of the following lines.
(a) y = 3x – 6
(b) 2x + 4y = 8
10. Find the equation of each line, write the equation in the form y = mx + c.
(a) Slope = 
1
, through (2,– 6 )
2
(b) Through (–3,2) and (1,10)
11. State whether the following pairs of lines are parallel or not.
(a) y – 3x = 5 and 2y + 8 = 6x
(b) y = 3 and y = 2
Bonus Question
(a) What is its height after 20 minutes?
(b) How fast is the balloon rising every minute?
Height ,h (feet)
12. A hot-air balloon is rising slowly.
The illustration below shows its height at 5-minute intervals for 20 minutes.
120
100
80
60
40
20
0
0
5
10
15
20
25
Time, t (minutes)
(c) Find the equation that represents the height, H, at time, t.
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Olympic College Math 94 – Test on Topics 6, to 8
Math 94 – Test on Topics 6 to 8 Solutions
1.
Plot each point: A(2,4), B(– 2, –4), C(0, – 4)
y
5
A
4
3
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
B
-3
-4
-5
C
2. Find the missing value of x that makes (x, – 6) a solution to the equation:
y =
–6 =
2 =
1
y = 2x – 8
2x – 8
2x – 8
2X
= x
3. (a) Determine which of the three ordered pairs does not satisfy the given equation.
Equation: 2x – 3y = 9
Points: (3,-2.5) (0, – 3) (– 3, – 5)
For the point (3,-2.5)
2x – 3y
= 9
2(3) – 3(-2.5) = 9
6 + 7.5 = 9
13.5
= 9
For the point (0, – 3)
2x – 3y
= 9
2(0) – 3(-3) = 9
0+9 = 9
9 = 9
For the point (– 3, – 5)
2x – 3y
= 9
2(-3) – 3(-5)
= 9
- 6 + 15
= 9
9
= 9
This point does not work
This point works
This point works
(b) Plot the points that satisfy the equation and draw a straight line through the points:
y
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
-2
1 2 3 4 5
x
-3
-4
-5
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Olympic College Math 94 – Test on Topics 6, to 8
y
4. Graph the line y = – 3
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
-3
-4
-5
5. Graph the line 2x – 3y = 12, using the x-intercepts and y-intercepts:
y
Choose x = 0
2x – 3y
2(0) – 3y
0 – 3y
- 3y
y
=
=
=
=
=
5
12
12
12
12
-4
This is the point (0, - 4)
4
3
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
1
2
3
-2
Choose y = 0
-3
2x – 3y
2x – 3(0)
2x – 0
2x
x
=
=
=
=
=
12
12
12
12
6
-4
-5
This is the point (6, 0)
y
6. (a) By calculating the rise and the run find the slope of this line..
Run = 75
4
7
Slope =
= 1
3
7
2
Rise = 7
1
(b) What are the coordinates of the y-intercept?
y-intercept = (0,1)
(c) Write down the equation of this line.
y=x+1
-5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
4
5
x
Page | 6
Olympic College Math 94 – Test on Topics 6, to 8
7.
For computer repairs, a technician charges a flat fee of $25.50, plus $20 per hour required for the
repair.
(a)
Write an equation for the cost, C, she charges in terms of hours required, h.
C = 20h + 25.50
(b)
How much will it cost for a 3 hour repair?
C = 20h + 25.50 =
(c)
8.
20(3) + 25.50
=
60 + 25.50
=
$85.50
If you get $225.50 bill how many hour did the technician work for?
C
=
225.50
200
10
=
=
=
20h + 25.50
20h + 25.50
20h
h
Find the slope of the line through the points
(a) (– 5, – 1) and (10,6)
Slope
=
y 2  y1
=
x 2  x1
6  (1)
10  (5)
=
7
15
(b) (3, – 3) and (– 3 , – 3)
Slope
=
y 2  y1
=
x 2  x1
 3  (3)
33
=
0
=0
6
9. What is the slope and the coordinates of the y-intercept for each of the following lines.
(a) y = 3x – 6
(b) 2x + 4y =
4y
=
y
=
y
=
Slope = 3
8
-2x + 8
 2x  8
2
- 0.5x + 2
Slope = - 0.5
y-intercept (0,-6)
y-intercept (0,2)
10. Find the equation of each line, write the equation in the form y = mx + c.
(a) Slope = 
y – y2
1
, through (2,– 6 )
2
=
y – (–6) =
y+6
=
y
=
m(x – x2)
1
(x – 2)
2
1
 x+1
2
1
 x–5
2

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Olympic College Math 94 – Test on Topics 6, to 8
10.(b) Through (–3,2) and (1,10)
Slope
y 2  y1
=
x 2  x1
=
10  2
=
1  (3)
8
4
=
2
Slope =2, through (1,10 )
y – y2
y – 10
y – 10
y
=
=
=
=
m(x – x2)
2(x – 1)
2x – 2
2x + 8
11. State whether the following pairs of lines are parallel or not.
(a) y – 3x = 5 and 2y + 8 = 6x
y = 3x + 5
2y + 8
2y
y
=
=
=
so its slope is 3
6x
6x – 8
3x – 4
(b) y = 3 and y = 2
so its slope is 3 , this means that these two lines are parallel.
Both are horizontal lines, this means that these two lines are parallel.
Bonus Question
(a) What is its height after 20 minutes?
Answer = 100 feet
(b) How fast is the balloon rising every minute?
Answer: Increase of 40 feet in 20 minutes
this is 2 feet per minute
(c) Find the equation that represents the height
H, at time, t.
Height ,h (feet)
12. A hot-air balloon is rising slowly.
The illustration below shows its height at 5-minute intervals for 20 minutes.
120
100
80
60
40
20
0
0
5
10
15
20
25
Time, t (minutes)
Answer H = 2t + 60
Page | 8