smithmorgan773p35885
28.03.2021 •
Mathematics
A unit rate is a rate in which the first term is compared to
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Ответ:
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.