Respuesta :
Answer with explanation:
Equation of line passing through two points ,
[tex](x_{1}, y_{1}), \text{and} (x_{2}, y_{2}) \text{is}\\\\ \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Equation of line passing through the points (4, 5) and (10, 2) is
[tex]\Rightarrow \frac{y-5}{x-4}=\frac{5-2}{4-10}\\\\\Rightarrow \frac{y-5}{x-4}=\frac{3}{-6}\\\\\Rightarrow \frac{y-5}{x-4}=\frac{1}{-2}\\\\\Rightarrow -2y+10=x-4\\\\\Rightarrow x+2 y-4-10=0\\\\\Rightarrow x +2 y-14=0[/tex]
To Find the inverse of the function obtained below
[tex]x+2 y-14=0\\\\2 y=14 -x\\\\y=\frac{14-x}{2}\\\\ \text{Replace x by y and y by x to obtain inverse of the function}\\\\x=\frac{14-y}{2}\\\\ 2 x=14-y\\\\2 x+y=14[/tex]
⇒⇒The equation
2 x + y=14
represents an inverse variation function that passes through the points (4, 5) and (10, 2).
