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Question 375101: I may have this one figured out. I will show you what I have so far. The question is Determine whether the graphs of each pair of lines are parallel.
2x+4 = y and
2y = 4x - 7.
I worked them out as the first line being 2 for the slope and the second being -7/2. I think these lines are NOT parallel because the slopes are different for each.
Thank you.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Given the values you determined for the slope, you came to the correct conclusion. Whenever the slopes are NOT equal, the lines are NOT parallel. Unfortunately, you made an error when calculating the slope for the second equation. The slope for the first equation is indeed 2 as a simple swap of sides shows us:
And we can see that with the equation in slope-intercept form,  , that the coefficient on  , and therefore the slope, is 2.
But if you solve the other equation for  by dividing both sides by 2, you get
And the coefficient on is again 2, so the slope of the second line is also 2. What is different is the -intercept, that is, the constant term. This tells us that even though the two lines have the same slope, the place they intersect the -axis is different. Hence, these two lines are indeed parallel (as opposed to being the same line)
See?
John
My calculator said it, I believe it, that settles it
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