Question

The graphs of the two linear equations ax + by = c and bx - ay = c, where a, b and c are all not equal to zero,

• A. are parallel
• B. intersect at one point but not perpendicular
• C. intersect at two points
• D. perpendicular

Answer 1

The correct option is D perpendicular

The given equations are,

$ax+by=c$

$\Rightarrow$ $y=\frac{-a}{b}x+\frac{c}{b}$ ----- ( 1 )

$bx-ay=c$

$\Rightarrow$ $y=\frac{b}{a}x-\frac{c}{a}$ ----- ( 2 )

Comparing equation ( 1 ) and ( 2 ) with, $y=mx+b$ we get,

$\Rightarrow$ $m_1=\frac{-a}{b}$ [ From ( 1 ) ]

And from equation ( 2 ),

$\Rightarrow$ $m_2=\frac{b}{a}=\frac{-1}{m_1}$

When the slopes of two lines are the negative inverse of one another, then they are perpendicular lines.

$\therefore$ The relationship between two linea is that they are perpendicular.