ds - coordinate geometry

[ccassel]

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,

[MAAJ]

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

[ccassel]

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,

[MAAJ]

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)

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,

[ccassel]

I see, the "1-m" is used to make you think there is another unknown variable when in fact "m" can be solved with equation "m=1-m".

Thank you Maaj!