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