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secondweb448
30.05.2021 •
Mathematics
Consider the equations below:
y = 2x and 6x = 3y + 5
Are the lines parallel or perpendicular?
A Parallel because the product of the slopes is -1.
B Parallel because the slopes are the same.
C Perpendicular because the product of the slopes
is -1.
D Perpendicular because the slopes are the same.
Solved
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Ответ:
Explanation:
Let's solve 6x = 3y + 5 for y
6x = 3y + 5
6x-5 = 3y
3y = 6x-5
y = (6x-5)/3
y = (6x)/3 - (5/3)
y = 2x - (5/3)
This final equation is in the form y = mx+b with m = 2 as the slope and b = -5/3 as the y intercept.
With the equation y = 2x, aka y = 2x+0, the m and b values are m = 2 and b = 0 respectively.
We see that both equations have the same slope (m = 2), but different y intercepts. Therefore, the two lines are parallel. If both y intercepts were the same as well, then we'd be talking about the same identical line.
If the slopes multiplied to -1, then the lines are perpendicular. In any other case, the two lines are neither parallel nor perpendicular.
Ответ:
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