xy-plane

Case A:

y=ax + c1 (line l)
y=bx + c2 (line 2)

4 unknowns initially and with ab=-1, a or b cannot be solved

Case B:
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K passes through origin. We can get K's slope y2-y1/x2-x1

A & B together, we can find line l's slope without any problem

statement 1:

From this statement we know that the lines are perpendicular sce the product of the slopes is equal to -1...

But we cant determine the slope of line l

Insufficient

statement 2:

Line k passes through the origin..
with this we cant find the slope of line k

Combining both the statements we get

the slope of k can be determined
slope of k=change in y co-ordinates/change in x co-ordinates=
(12/5-0)/(16/5-0)=3/4
slope of k=3/4

product of the slopes of line l and k is -1
(3/4)*l=-1
l=-4/3
The slope of line l is -4/3

Hence C should be the ans

beater 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.

Equation of line for K, y=m1x + c1
Equation of line for L, y=m2x + c2

Value of m2 is? This we have to identify.
Given information. l and k intersect at (16/5,12/5)

Statement A: m1 * m2 = -1. Insufficient.

Statemetn B: Line K passes through origin. (0,0) and (16/5,12/5). therefor m1=3/4. But we need to identify the value of m2. So it is Insufficient.

Both statements together are sufficient. Answer C.