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.
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
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
. Not sufficient.
(1)+(2) We can calculate the slope of k
and we know that the product of the slopes of l
is -1, so we can calculate the slope of line l
For more on these issues check Coordinate Geometry chapter of Math Book (link in my signature).
Hope it helps.
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