we know that
The rate of the Relationship is the slope of the function
so
Find the slope of the Relationship A
the slope is equal to
[tex] m=\frac{(y2-y1)}{(x2-x1)}[/tex]
we have the points
[tex] (4,2)\ and\ (8,4)[/tex]
Substitute in the formula above to find the slope
[tex] m=\frac{(4-2)}{(8-4)}[/tex]
[tex] m=\frac{2}{4}=0.5[/tex]
Compare the value of the rate of the Relationship A with each case
case a)
[tex] y = (3/4)x[/tex]
In this case the rate of the equation is equal to [tex] \frac{3}{4}[/tex]
Compare with the rate of the Relationship A
[tex]\frac{3}{4}>\frac{2}{4}[/tex]
therefore
[tex] y = (3/4)x[/tex] -----> This equation could represent Relationship B
case b)
[tex]y = (0.6)x[/tex]
In this case the rate of the equation is equal to [tex] 0.6 [/tex]
Compare with the rate of the Relationship A
[tex] 0.6 > \frac{2}{4}[/tex]
[tex] 0.6 > 0.5[/tex]
therefore
[tex] y = (0.6)x[/tex] -----> This equation could represent Relationship B
case c)
[tex] y = (2/3)x[/tex]
In this case the rate of the equation is equal to [tex] (2/3)[/tex]
Compare with the rate of the Relationship A
[tex] \frac{2}{3} >\frac{2}{4}[/tex]
Multiply by [tex] 12[/tex] both sides
[tex] 8 > 6[/tex]
therefore
[tex] y = (2/3)x [/tex] -----> This equation could represent Relationship B
case d)
[tex] y = (1/4)x[/tex]
In this case the rate of the equation is equal to [tex] (1/4)[/tex]
Compare with the rate of the Relationship A
[tex] \frac{1}{4} <\frac{2}{4}[/tex]
therefore
[tex] y = (1/4)x[/tex] -----> This equation could not represent Relationship B
therefore
the answer is
[tex] y = (3/4)x[/tex]
[tex] y = (0.6)x[/tex]
[tex] y = (2/3)x[/tex]
