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

The graph in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

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

The linear equation is equal to

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

The other point is (8,3)

Plot the points and join them to draw the line

The graph in the attached figure

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

where's the diagram?

step-by-step explanation: