Chapter ISG, Problem 4.2STP

To determine

To calculate which line functions are inverse of each other.

Answer to Problem 4.2STP

  $y=2x-3$ and $y=0.5x+1.5$ are inverse to each other

Explanation of Solution

Given information: the given equations are,

  $y=2x+3$ , $y=2x-3$ , $y=-0.5x+0.5$ and $y=0.5x+1.5$

Writing the “x”in term of “y” in the first equation,

Shifting left hand side variable to right hand side,

  $2x=y-3$

Cross-multiplying,

  $x=\frac{1}{2}y-\frac{3}{2}$

On solving,

  $x=0.5y-1.5$ ______________(1)

Writing the “x” in term of “y” in the second equation,

Shifting left hand side variable to right hand side,

  $2x=y+3$

Cross-multiplying,

  $x=\frac{1}{2}y+\frac{3}{2}$

On solving,

  $x=0.5y+1.5$ ______________(2)

Comparing (1) and (2) with the third and fourth equation,

(2) and fourth equation are similar, as their constants are same.

Therefore,

  $y=2x-3$ and $y=0.5x+1.5$ are inverse to each other