udaymathapati wrote:

In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?

(1) The product of the slopes of line l and line k is –1.

(2) Line k passes through the origin.

Line

l passes through the point (16/5, 12/5). If we knew some other point through which line

l passes then we would be able to calculate the slope: the slope is defined as

the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.

(1) The product of the slopes of line

l and line

k is -1 --> line

l and

k are perpendicular to each other (the two lines are perpendicular if and only the product of their slopes is -1). Not, sufficient, as we can have infinite # of perpendicular lines passing through some point (16/5, 12/5).

(2) Line

k passes through the origin --> we have the second point for line

k, so we can calculate the slope of

k, but we don't know the relationship between the lines

l and

k. Not sufficient.

(1)+(2) We can calculate the slope of

k and we know that the product of the slopes of

l and

k is -1, so we can calculate the slope of line

l too. Sufficient.

Answer: C.

For more on these issues check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.

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