Question

Which equation represents an inverse variation function that passes through the points (4, 5) and (10, 2)?

Answer 1

Answer with explanation:

Equation of line passing through two points ,

`(x_(1), y_(1)), \text{and} (x_(2), y_(2)) \text{is}\\\\ (y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1))`

Equation of line passing through the points (4, 5) and (10, 2) is

`\Rightarrow (y-5)/(x-4)=(5-2)/(4-10)\\\\\Rightarrow (y-5)/(x-4)=(3)/(-6)\\\\\Rightarrow (y-5)/(x-4)=(1)/(-2)\\\\\Rightarrow -2y+10=x-4\\\\\Rightarrow x+2 y-4-10=0\\\\\Rightarrow x +2 y-14=0`

To Find the inverse of the function obtained below

`x+2 y-14=0\\\\2 y=14 -x\\\\y=(14-x)/(2)\\\\ \text{Replace x by y and y by x to obtain inverse of the function}\\\\x=(14-y)/(2)\\\\ 2 x=14-y\\\\2 x+y=14`

⇒⇒The equation

2 x + y=14

represents an inverse variation function that passes through the points (4, 5) and (10, 2).