Relationship B has a greater rate than Relationship A. The graph represents Relationship A.
Which equations could represent Relationship B?
Choose all answers that are correct.
A. y = 3/4x
B. y = 0.6x
C. y = 2/3x
D. y = 1/4x
Help Meh
Answer (2)
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 = ( x 2 − x 1 ) ( y 2 − y 1 )
we have the points
( 4 , 2 ) an d ( 8 , 4 )
Substitute in the formula above to find the slope
m = ( 8 − 4 ) ( 4 − 2 )
m = 4 2 = 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 4 3
Compare with the rate of the Relationship A
\frac{2}{4}"> 4 3 > 4 2
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
\frac{2}{4}"> 0.6 > 4 2
0.5"> 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}{4}"> 3 2 > 4 2
Multiply by 12 both sides
6"> 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
4 1 < 4 2
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
The equations that could represent Relationship B, which has a greater rate than Relationship A, are A (y = 3/4x), B (y = 0.6x), and C (y = 2/3x). Option D (y = 1/4x) does not qualify because its slope is less than that of Relationship A.
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