If a line K passes through (1, 5) and the line K intersects with the

Solution

Step 1: Analyse Question Stem

• Let’s say line K is \(y=m_1x+c_1 \), and line L is \(y = m_2x+c_2 \), where

o \(m_1 \) and \(m_2\) are slopes of K and L respectively, and
o \(c_1\) and \(c_2 \) are y intercepts of K and L respectively.
• Line K passes through (1,5), so
o \(1=m_1*5+c_1 ……………..Eq.(1)\)
• Lines K and L intersect each other at (5,t)
o So, point (5,t) will satisfy equation of line K as well as L.
We need to find the value of t; which can be found if we know the equation of any one of the lines K and L.



Step 2: Analyse Statements Independently


Statement 1: The y-intercept of the line K is 5

• According to this statement, \( c_1 = 5\)
• On substituting the value of \(c_1\) in Eq.(1) , we get : \(m_1 = \frac{-4}{5}\)
• So , Equation of line K is \(y=\frac{-4}{5}x+5\)
Since, we got equation of line K, then we can substitute x=5 and y=t in it and can easily find the value of t.
Hence, statement 1 is sufficient and we can eliminate answer options B, C and E
Statement 2: The slope of the line L is positive

• According to this statement \(m_2 >0\)