we have that
1) Relationship B has a lesser rate than Relationship A
2) The graph represents Relationship A
we know that
The rate is equal to the slope of the linear equation in the graph
Step 1
Find the slope of the Relationship A
we have
\(A(1,3)\\B(2,6)\)
we know that
The formula to find the slope m between two points is equal to
\(m=\frac{(y2-y1)}{(x2-x1)}\)
substitute the values
\(m=\frac{(6-3)}{(2-1)}\)
\(m=\frac{(3)}{(1)}\)
\(mA=3\)
Step 2
Find the equation that could represent Relationship B
we know that
Relationship B has a lesser rate than Relationship A
so
the slope of the Relationship B is less to the slope of the Relationship A
\(mB < 3\)
therefore
the answer is
\(y=x\) ------> because the slope is \(1\)
\(y=(3/2)x\) ------> because the slope is \(1.5\)
