Question

Which graph shows a proportional relationship in which the value of y is one-half of the value of x?

Answer 1

The graph is shown below.

Explanation:

Given:

The relationship between the variables 'x' and 'y' is proportional relationship.

A proportional relationship is of the form:

`y=mx`

Where 'm' is called the constant of proportionality and also the slope of the line
`y=mx`

Now, it is given that 'y' is one-half of the value of 'x'. Framing it in equation form, we get:

`y=(1)/(2)x`

So, the slope of the line is
`m=(1)/(2)`

Slope is nothing but rise over run. Run is parallel the x-axis and rise is parallel to the y-axis.

Now, a proportional relationship always passes through the origin.

So, in order to get slope equal to one-half, we need to move 2 units along the x-axis from the origin and then 1 unit parallel to y-axis to get to the next point. The point is (2, 1).

Now, we draw a line passing through the origin and (2, 1) which is the required of the given proportional relationship.