C


1: we dont know anything about the other line but we can find the slope of line l = 2

2: again we dont know the other line's slope but k's is -1/2

Together 2*-1/2= -1

But you could just realize that 1 and 2 are suff together b/c we know the slopes we are going to get a YES OR A NO NOT BOTH. so u could save some time.

>> Line K has x-intercept 4 and y-intercept 2.

Its not clear if the x-intercept is going to be a (4,0). All it said is that x-intercept is 4 and y-intercept is 2. Even a coordinate of (-4,0) equals an x-intercept of 4.



So the x coordinates can be (4,0) or (-4,0) and y coordinates can be (0,2) or (0,-2)

So there are two possible lines that are perpendicular and the other 2 are not.

So in my opinion E.

What is the OA ?
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what do u mean by 2 has to have a specific set of cordinates .. form what i see i agree to your earlier assumption ...when u say line k has 4 as x cordinate and 2 as y cordinate u can very well say that it is a cordinate of the same point (4,2) then u cannot say anything about K's slope as it just passes through one point .. please explain as i still feel it should be E

We don't need to calculate anything to answer this question.

If L and K are lines in xy- plane, is the product of the slope of l and k equal to -1?

The product of two lines equal to -1 if these lines are perpendicular to each other. So, the question basically asks whether L and K are perpendicular to each other.

Now, if we knew the equations of each line we would be able to answer the question. What do we need to find equation of a line? Since a line is defined by two points, then if we knew any two points of a line then we could get its equatiom

(1) Line L passes through the origin and the point (1,2). We have two points of line L: (0, 0) and (1, 2). So, we can get the equation of line L, though we know nothing about line K. Not sufficient.

(2) Line K has x-intercept 4 and y-intercept 2. We have two points of line K: (4, 0) and (0, 2). So, we can get the equation of line K, though we know nothing about line L. Not sufficient.

(1)+(2) We know both equation, hence we can answer whether the lines are perpendicular to each other. Sufficient.

Answer: C.



Given two points (x_1,y_1) and (x_2,y_2) on a line, the slope m of the line is:

m=\frac{y_2-y_1}{x_2-x_1}.

Since x-intercept of line K is 4, then it passes through point (4, 0) and since y-intercept of line K is 2, the it passes through point (0, 2). Hence it's slope is m=\frac{2-0}{0-4}=-\frac{1}{2}.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

Hope it helps.
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