Adirect variation includes the points (4,20) and (1,n). find n

In direct variation of points from (4,20) to  (1,n). value of n will be equal to 5.

Direction variation means that , In coordinate points , both x and y value will be multiplied or divide by the same number.

In given points  (4, 20)  and (1, n) . It is observed that, x - value i.e. 4 changes to 1 . it means that x value , 4 is divide by 4 .

So, y value is also divide by 4.

Therefore,    

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n = 5

Step-by-step explanation:

As we go from point (1, n) to point (4, 20), x increases by 3 and n increases to 20; we don't yet know by how much.  The the slope of the line representing this direct variation is

m = rise / run = 4 - 1   /   20 - n

We can now write a tentative equation of the line, using the slope-intercept form:

y = mx + b becomes mx + 0, or just mx, because a direct variation has no y-intercept.

We can now set y = mx, replacing y with 20 and x with 4:

           4-1

20 = (4)

           20-n

                3

or:   5 =

              20 - n

This yields 100 - 5n = 3, or 97 = 5n.    Thus, n = 97/5

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Start with the slope-intercept form of the equation of a straight line:

y = mx + b.  Next, let b = 0, since a direct variation intercepts the y-axis in the point (0, 0).

Then y = mx + 0, or just y = mx.  Let's use data from the given point (4, 20):

20 = m(4), or m = 5.

Another formula for slope is m = rise / run.  Here, the rise is 20 - n and the run is 4-1, or, after simplification, m = (20 - n)/3.

We need to determine the value of n.  To do this, equate m = (20 - n)/3 to 5 (which was found a few lines earlier).

         20-n

Then = 5, and after mult. both sides by 3, we get 20-n = 15.

             3

Subtracting 15 from 20 results in 5 - n = 0, so we see that n = 5.