Olympic College Math 94 – Test on Topics 6, to 8

Math 94 – Test on Topics 6 to 81.

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)

-1

-2

-3

-4

-5

-5 -4 -3 -2 -1 0 1 2 3 4 5x

Plot each point: A(2,4), B(– 2, –4), C(0, – 4)

y

5

4

3

2

1

-1

-2

-3

-4

-5

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-5 -4 -3 -2 -1 0 1 2 3 4 5x

(b) Plot the points that satisfy the equation and draw a straight line through the points:y

5

4

3

2

1

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4. Graph the line y = – 3

(b) What are the coordinates of the y-intercept?

(c) Write down the equation of this line.

5

4

3

2

1

-5 -4 -3 -2 -1 0 1 2 3 4 5x

Olympic College Math 94 – Test on Topics 6, to 8

y

-5 -4 -3 -2 -1 0 1 2 3 4 5x

-1

-2

-3

-4

-5

5. Graph the line 2x – 3y = 12, using the x-intercepts and y-intercepts:

y

5

4

3

2

1

-3

-4

-5

-1

-2

2

1

-5 -4 -3 -2 -1 0 1 2 3 4 5x

-1

-2

-3

-4

-5

6. (a) By calculating the rise and the run find the slope of this line..

y

5

4

3

Olympic College Math 94 – Test on Topics 6, to 8

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7. For computer repairs, a technician charges a flat fee of $25.50, plus $20 per hour required for therepair.

(a)

(b)

(c)

Write an equation for the cost, C, she charges in terms of hours required, h.

How much will it cost for a 3 hour repair?

If you get $225.50 bill how many hour did the technician work for?

8. Find the slope of the line through the points

(a) (– 5, – 1) and (10,6)

(b) (3, – 3) and (– 3 , – 3)

Hei

ght

,h (

feet

)

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.1

2(a) Slope = , through (2,– 6 )

(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 Question12. A hot-air balloon is rising slowly.

The illustration below shows its height at 5-minute intervals for 20 minutes.

(a) What is its height after 20 minutes?

(b) How fast is the balloon rising every minute?

120100

80604020

00 5 10 15 20 25

Time, t (minutes)

(c) Find the equation that represents the height, H, at time, t.

Page | 4

Page | 5

Olympic College Math 94 – Test on Topics 6, to 8

Math 94 – Test on Topics 6 to 8 Solutions1. Plot each point: A(2,4), B(– 2, –4), C(0, – 4)

2. Find the missing value of x that makes (x, – 6) a solution to the equation: y = 2x – 8

y = 2x – 8– 6 = 2x – 82 = 2X1 = 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) For the point (0, – 3) For the point (– 3, – 5)2x – 3y = 9 2x – 3y = 9 2x – 3y = 9

2(3) – 3(-2.5) = 9 2(0) – 3(-3) = 9 2(-3) – 3(-5) = 96 + 7.5 = 9 0+9 = 9 - 6 + 15 = 913.5 = 9 9 = 9 9 = 9

This point does not work This point works This point works

-3

-4

-5

-1

-2

-5 -4 -3 -2 -1 0 1 2 3 4 5x

y

5

4

3

2

1

A

BC

-5 -4 -3 -2 -1 0-1

-2

-3

-4

-5

1 2 3 4 5x

(b) Plot the points that satisfy the equation and draw a straight line through the points:y5

4

3

2

1

Rise = 7

Olympic College Math 94 – Test on Topics 6, to 8

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4. Graph the line y = – 3

Choose x = 0

2x – 3y2(0) – 3y

0 – 3y- 3y

y

=====

12121212-4

This is the point (0, - 4)

Choose y = 0

2x – 3y2x – 3(0)

2x – 02x

x

=====

121212126

This is the point (6, 0)

6. (a) By calculating the rise and the run find the slope of this line..

Slope =7

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

-1

-2

-3

-4

-5

5. Graph the line 2x – 3y = 12, using the x-intercepts and y-intercepts:

-5 -4 -3 -2 -1 0 1 2 3 4 5x

y

5

4

3

2

1

-4

-5

-2

-3

5

4

3

2

1

-5 -4 -3 -2 -1 0-1

1 2 3 4 5x

y

-3

-4

-5

2

1

-5 -4 -3 -2 -1 0-1

-2

1 2 3 4 5x

y

Run = 754

3

Olympic College Math 94 – Test on Topics 6, to 8

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7. For computer repairs, a technician charges a flat fee of $25.50, plus $20 per hour required for therepair.

(a)

(b)

Write an equation for the cost, C, she charges in terms of hours required, h.

C = 20h + 25.50

How much will it cost for a 3 hour repair?

C = 20h + 25.50 = 20(3) + 25.50 = 60 + 25.50 = $85.50

(c) If you get $225.50 bill how many hour did the technician work for?

C225.50

20010

====

20h + 25.5020h + 25.5020hh

8. Find the slope of the line through the points

(a) (– 5, – 1) and (10,6) Slope = y 2 y1

x2 x1

=6 (1)

10 (5)=

7

15

(b) (3, – 3) and (– 3 , – 3) Slope = y 2 y1

x2 x1

= 3 (3)

3 3=

0

6=0

9. What is the slope and the coordinates of the y-intercept for each of the following lines.

Slope = 3 y-intercept (0,-6)(a) y = 3x – 6

(b) 2x + 4y = 84y

y

=

=

-2x + 8 2 x 8

2y = - 0.5x + 2 Slope = - 0.5 y-intercept (0,2)

10. Find the equation of each line, write the equation in the form y = mx + c.1

2(a) Slope = , through (2,– 6 )

y – y2 = m(x – x2)

y – (–6) =1

2 (x – 2)

y+6

y

=

=

1

21

2

x+1

x – 5

Hei

ght ,

h (f

eet)

Olympic College Math 94 – Test on Topics 6, to 8

10.(b) Through (–3,2) and (1,10) Slope = y 2 y1

x2 x1

=10 2

1 (3)=

8

4= 2

Slope =2, through (1,10 )

y – y2

y – 10y – 10y

====

m(x – x2)2(x – 1)2x – 22x + 8

11. State whether the following pairs of lines are parallel or not.

(a) y – 3x = 5 and 2y + 8 = 6x

y = 3x + 5 so its slope is 3

2y + 82y

==

6x6x – 8

y = 3x – 4 so its slope is 3 , this means that these two lines are parallel.

(b) y = 3 and y = 2 Both are horizontal lines, this means that these two lines are parallel.

Bonus Question12. A hot-air balloon is rising slowly.

The illustration below shows its height at 5-minute intervals for 20 minutes.

(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 minutesthis is 2 feet per minute

(c) Find the equation that represents the heightH, at time, t.

Answer H = 2t + 60

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120100

80604020

00 5 10 15 20 25

Time, t (minutes)