Two line l and k intersect at a point (4, 3). Is the product of their slopes -1?
(1) x intercepts of line l and k are positive
(2) y intercept of line l and k are negative
OA B
Source: Princeton Review
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Two line l and k intersect at a point (4, 3). Is the product
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$$For\ line\ l;\ y=m_lx+b_l\ where\ y=4\ and\ x=3$$
$$4=3m_l+b_l$$
$$For\ line\ k;\ y=m_kx+b_k\ where\ y=4\ and\ x=3$$
$$4=3m_k+b_k$$
So, the question=> is the product of their slopes -1?
$$That\ is,\ is\ m_l\cdot m_k=-1?$$
Statement 1: x intercepts of line l and k are positive
This means that 'x' intercepts > 0
we have 'x' intercept when y=0
Thus, this tells us nothing about the slope of either line L or line K, and with the given conditions, we cannot evaluate the product of Ml * Mk.
Hence, statement 1 is NOT SUFFICIENT.
Statement 2: y-intercept of line l and k are negative.
This means that y-intercept < 0 and at the same time Bl and Bk are both negative. This will require both line l and k travel upwards in order to get point (4,3).
Hence, both slopes will be positive, even though we don't know the actual value of both slopes, the product of positive numbers will yield a positive number.
$$Therefore,\ m_l\cdot m_k\ne-1$$
So, statement 2 alone is SUFFICIENT.
Answer to the problem is option B.
$$4=3m_l+b_l$$
$$For\ line\ k;\ y=m_kx+b_k\ where\ y=4\ and\ x=3$$
$$4=3m_k+b_k$$
So, the question=> is the product of their slopes -1?
$$That\ is,\ is\ m_l\cdot m_k=-1?$$
Statement 1: x intercepts of line l and k are positive
This means that 'x' intercepts > 0
we have 'x' intercept when y=0
Thus, this tells us nothing about the slope of either line L or line K, and with the given conditions, we cannot evaluate the product of Ml * Mk.
Hence, statement 1 is NOT SUFFICIENT.
Statement 2: y-intercept of line l and k are negative.
This means that y-intercept < 0 and at the same time Bl and Bk are both negative. This will require both line l and k travel upwards in order to get point (4,3).
Hence, both slopes will be positive, even though we don't know the actual value of both slopes, the product of positive numbers will yield a positive number.
$$Therefore,\ m_l\cdot m_k\ne-1$$
So, statement 2 alone is SUFFICIENT.
Answer to the problem is option B.
