Question

in a proportional relationship the ratio y/x is constant. Show that this ratio is not constant for the equation y=a-14

Answer 1

To show that the ratio $\frac{y}{x}$ is not constant for the function $y=a-14$ we only need to evaluate this function at 2 points and then show that the ratio is not the same for those two points. Note that here $a$ represents $x$.  

To find the counter examples here, I will use the values $a=20$  and $a=28$. For $a = 20$ , the equation tells us that the output is

$y=20-14=6$. For this value of $a$ the point is point is $(20,6)$. The ratio $\frac{y}{x} =\frac{6}{20}$. For the $a=28$, $y=28-14=14$. For this value of $a$ the  point is $(28,14)$ . The ratio $\frac{y}{x} =\frac{14}{28} =\frac{1}{2}$. Clearly this ratio is not constant for all ordered pairs.