Bunuel wrote:
pavanpuneet wrote:
With condition 1, when we try to solve algebraic way:
x intercept of line m : -b1/m1>1
and for line b : -b2/m2<1
Given that we do not the sign of slopes m1 and m2, we cant cross multiply, then how do we proceed after this condition?
ALGEBRAIC APPROACH.
Line m and n pass through point (1,2). Is the slope of m greater than the slope of n? Given: lines \(y_m=mx+b\) and \(y_n=nx+c\) pass through point (1,2). Hence: \(2=m+b\) and \(2=n+c\).
Question asks: is \(m>n\)?
(1) The x-intercept of m is greater than 1 and that of n is less than 1. The x-intercept is the value of \(x\) when \(y=0\), so from this statement we have that:
\(-\frac{b}{m}>1\). Now, since from the stem \(b=2-m\), then \(-\frac{2-m}{m}>1\) --> \(\frac{m-2}{m}>1\) --> \(\frac{m}{m}-\frac{2}{m}>1\) --> \(1-\frac{2}{m}>1\) --> \(\frac{2}{m}<0\) --> \(m<0\);
\(-\frac{c}{n}<1\). Now, since from the stem \(c=2-n\), then \(-\frac{2-n}{n}<1\) --> \(\frac{n-2}{n}<1\) --> \(\frac{n}{n}-\frac{2}{n}<1\) --> \(1-\frac{2}{n}<1\) --> \(\frac{2}{m}>0\) --> \(n>0\);
So, we have that \(m<0<n\). Sufficient.
(2) The y-intercept of m = 4 and that of n = (-2). The y-intercept is the value of \(y\) for \(x=0\), so from this statement we have that:
\(b=4\). Now, since from the stem \(b=2-m\), then \(4=2-m\) --> \(m=-2\);
\(c=-2\). Now, since from the stem \(c=2-n\), then \(-2=2-n\) --> \(n=4\);
So, we have that \(m=-2<4=n\). Sufficient.
Answer: D.
Hope it's clear.
Hi Bunel I shall try to give a easier approach.
If a line's X intercept is ''a'' what information we get from that . Line pasess through point (a,0)
similarly if a line's Y intercept is "b" what information we get from that . Line pasess through point (0,b)
and if a line pasess through points (x1,y1)and (x2,y2) we compute the slope of the line by (y2-y1)/x2-x1).
so let us apply this to the present question
Line m and n pass through point (1,2). Is the slope of m greater than the slope of n?
1.The x-intercept of m is greater than 1 and that of n is less than 1
so x intercept of m is greater than 1 so it should pass through points (>1,0) so let us assume its (2,0)
x intercept of n is less than 1 so it should pass through points (<1,0) so let us assume its (-1,0) you can actually take any point less than 1 even (0.9,0) also.
so now computing slope with slope formula you can find slope of n > slope of m hence sufficient.
2.The y-intercept of m = 4 and that of n = (-2)
i.e. m pasess through point (0,4) and n pasess through point (0,-2)
and you can straight away compute the slope and determine which is greater
IMP: It is important to understand what is meant by intercept
hope this helps
This would avoid the larger equations.
Give me kudos if this helps
1.