Question

Graph the line that represents a proportional relationship between Y And x where the unit rate of change of y with their respective x is 3/8. In other words a change of one unit in x corresponds to a change of 38 units and Y graph the line and write the equation of the line

Answer 1

`y=(3)/(8)x`

The graph in the attached figure

Explanation:

we know that

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

Remember that

The unit rate of change is the same as the slope

so

In this problem

`m=(3)/(8)`

The linear equation is equal to

`y=(3)/(8)x`

To graph the line we need two points

we have (0,0) because the line passes through the origin

Determine other point

assume a value of x and calculate the value of y

For x=8

`y=(3)/(8)(8)=3`

The other point is (8,3)

Plot the points and join them to draw the line

The graph in the attached figure