500Brat500
Answered

According to the graph, the relationship between the number of rose plants and the number of roses is Proportional Or Non Proportional

According to the graph, the relationship between the number of rose plants and the number of roses is Proportional Or Non Proportional class=

Verified Answer :

calculista

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form \(\frac{y}{x} =k\)

where

k is a constant

in this problem

Let

\(A(0,0)\\ B(1,5)\)

Find the slope m

\(m=\frac{(y2-y1)}{(x2-x1)}\)

Substitute the values in the formula

\(m=\frac{(5-0)}{(1-0)}\)

\(m=5\)

Find the equation of the line with m and the point A

\(y-y1=m(x-x1)\)

\(y-0=5*(x-0)\)

\(y=5x\)

so

\(\frac{y}{x} =5\)

x is the number of rose plants

y is the the number of roses

so

the relationship between the number of rose plants and the number of roses is equal to

\(\frac{x}{y} =\frac{1}{5}\)

the answer is

the relationship is proportional

Answer:

Let y represents the Number of roses and x represents the number of plants,.

As per the statement:

From the graph, the coordinates points are:

(0, 0)

(1, 5)

(2, 10)

(3, 15)

(4, 20)

Proportional relationship: If two quantities varies directly to each other i.e

if y varies proportional to x then;

\(y = kx\)            .....[1]  where, k is the constant of proportionality.

Substitute the given any coordinate points i.e, (3, 15) in [1] t o find k.

\(15 = 3k\)

Divide both sides by 3 we have;

5 = k

or

k = 5

Then, we get the equation:

\(y =5x\)           .....[2]

Check:

(2, 10)

Substitute in [2] we have;

10 = 2(5)

10 = 10       true.

Therefore, the relationship between the number of rose plants and the number of roses is Proportional relationship.

Related Questions