To show that the ratio [tex]\frac{y}{x}[/tex] is not constant for the function [tex]y=a-14[/tex] 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 [tex]a[/tex] represents [tex]x[/tex].
To find the counter examples here, I will use the values [tex]a=20[/tex] and [tex]a=28[/tex]. For [tex]a = 20[/tex] , the equation tells us that the output is
[tex]y=20-14=6[/tex]. For this value of [tex]a[/tex] the point is point is [tex](20,6)[/tex]. The ratio [tex]\frac{y}{x} =\frac{6}{20}[/tex]. For the [tex]a=28[/tex], [tex]y=28-14=14[/tex]. For this value of [tex]a[/tex] the point is [tex](28,14)[/tex] . The ratio [tex]\frac{y}{x} =\frac{14}{28} =\frac{1}{2}[/tex]. Clearly this ratio is not constant for all ordered pairs.
