Question 8 Points 3
Identify the functions whose lines are parallel.
0 3x + 2y = 45 and 8x + 4y = 135
x + y = 25 and 2x + y = 15
O 2x + 2y = 50 and 4x + 2y = 90
O 2x + 2y = 4 and 4x + 4y = 16

2x + 2y = 4 and 4x + 4y = 16

Step-by-step explanation:

For two lines to be parallel, they must have the same slope.

To determine the correct answer to the question, we shall determine the slope of each equation in the given options to see which have the same slope. This can be obtained as follow:

1st option:

3x + 2y = 45 and 8x + 4y = 135

We shall rearrange the above equations to look like y = mx + c

NOTE: m is the slope.

3x + 2y = 45

rearrange

2y = –3x + 45

Divide both side by 2

y = –3x/2 + 45/2

Slope (m) = –3/2

8x + 4y = 135

Rearrange

4y = –8x + 135

Divide both side by 4

y = –8x/4 + 135/4

Slope (m) = –8/4 = –2

The two equation has different slopes. Thus, they are not parallel.

2nd option:

x + y = 25 and 2x + y = 15

x + y = 25

Rearrange

y = –x + 25

Slope (m) = –1

2x + y = 15

Rearrange

y = –2x + 15

Slope (m) = –2

The two equations has different slopes. Thus, they are not parallel.

3rd option:

2x + 2y = 50 and 4x + 2y = 90

2x + 2y = 50

Rearrange

2y = –2x + 50

Divide both side by 2

y = –2x/2 + 50/2

Slope (m) = –2/2 = –1

4x + 2y = 90

Rearrange

2y = –4x + 90

Divide both side by 2

y = –4x/2 + 90/2

Slope (m) = –4/2 = –2

The two equations has different slopes. Thus, they are not parallel.

4th option:

2x + 2y = 4 and 4x + 4y = 16

2x + 2y = 4

Rearrange

2y = –2x + 4

Divide both side by 2

y = –2x/2 + 4/2

Slope (m) = –2/2 = –1

4x + 4y = 16

Rearrange

4y = –4x + 16

Divide both side by 4

y = –4x/4 + 16/4

Slope (m) = –4/4 = –1

The two equations have the same slopes. Thus, they are parallel.