Question

Which statement best explains if the graph correctly represents the proportional relationship y = 3.5x?

A graph of a coordinate plane is shown. Points are graphed at 1 comma 3.5 and 2 comma 7. The points are joined by a line.

No, the points shown on the line would not be part of y = 3.5x
No, proportions cannot be represented on a graph
Yes, the points shown on the line would be part of y = 3.5x
Yes, all proportions can be shown on the graph of this line

Answer 1

The answer to this question is yes, the points shown on the line would be part of y = 3.5x

Answer 2

It does, the points shown on the line would be part of
`y=3.5x`

Explanation:

see the attached figure to better understand the problem

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` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have

`y=3.5x`

The slope is equal to
`m=3.5` ------> is a positive slope

The line passes through the origin

therefore

This linear equation represent a proportional variation

Verify the values of the points of the graph with the equation

For
`x=1`

`y=3.5*1=3.5` -----> is correct

For
`x=2`

`y=3.5*2=7` -----> is correct