Hi,
How would you answer this question?
If line k in the xy-plane has equation y=mx+b, where m and b are constants, what is the slope of k?
(1) k is parallel to the line with equation y=(1-m)x+b+1
(2) k intersects the line with equation y=2x+3 at the point (2,7)
cheers,
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MAAJ
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IMO [spoiler](A)[/spoiler]
(1) Anything that multiplies x must be the slope in the slope-intercept equation. Because k is parallel to this other line, then line k MUST have the same slope. So m = (1-m) -> m = 1/2
(2) If line k intercept other line at some point, then it means that they have different slope. If they intersect at point (2,7) then x=2 and y=7 solve the equation for both lines. If we input this values in y = mx+b we get 7 = m2+b but still we don't have the slope. Line k can intercept line y = 2x+3 at point (2,7) from many different angles.
What's the OA? :p
(1) Anything that multiplies x must be the slope in the slope-intercept equation. Because k is parallel to this other line, then line k MUST have the same slope. So m = (1-m) -> m = 1/2
(2) If line k intercept other line at some point, then it means that they have different slope. If they intersect at point (2,7) then x=2 and y=7 solve the equation for both lines. If we input this values in y = mx+b we get 7 = m2+b but still we don't have the slope. Line k can intercept line y = 2x+3 at point (2,7) from many different angles.
What's the OA? :p
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ccassel
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You are correct, the answer is A.
(1) if k is parallel to the line with equation y=(1-m)x+b+1, how do you find the slope when you dont know what "m" is?
(2) this makes sense since line k could intercect at any angle.
cheers,
(1) if k is parallel to the line with equation y=(1-m)x+b+1, how do you find the slope when you dont know what "m" is?
(2) this makes sense since line k could intercect at any angle.
cheers,
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MAAJ
- Master | Next Rank: 500 Posts
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- Joined: Sun Jul 12, 2009 7:12 am
- Location: Dominican Republic
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Remember that in the slope-intercept equation, any term that multiplies x MUST be the slope.
Also two lines that are parallel, MUST have the same slope.
So m = (1-m) -> m = 1/2
If we plug this in the equation of line k, we get y = 1/2x+b
And if we plug this into the formula of STMT 1 we get y = [1-(1/2)]x+b+1 -> y =1/2x+b+1
So as you see both lines have the same slope. Both lines must be parallel, the only difference is that one line is +1 higher than the other in terms of y (this because x and b are both constant)
Also two lines that are parallel, MUST have the same slope.
So m = (1-m) -> m = 1/2
If we plug this in the equation of line k, we get y = 1/2x+b
And if we plug this into the formula of STMT 1 we get y = [1-(1/2)]x+b+1 -> y =1/2x+b+1
So as you see both lines have the same slope. Both lines must be parallel, the only difference is that one line is +1 higher than the other in terms of y (this because x and b are both constant)
ccassel wrote:You are correct, the answer is A.
(1) if k is parallel to the line with equation y=(1-m)x+b+1, how do you find the slope when you dont know what "m" is?
(2) this makes sense since line k could intercect at any angle.
cheers,
"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."
