Question

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

Answer 1

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.

Answer 2

we know that

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

where

k is a constant

in this problem

Let

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

Find the slope m

`m=((y2-y1))/((x2-x1))`

Substitute the values in the formula

`m=((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

`(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

`(x)/(y) =(1)/(5)`

the answer is

the relationship is proportional