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

Answer:n = 5Step-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 ism = rise / run = 4 - 1   /   20 - nWe 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:            4-120 = ------------ (4)            20-n                 3or:   5 = -----------               20 - nThis yields 100 - 5n = 3, or 97 = 5n.    Thus, n = 97/588888888888888888888888888888888888888888Start 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-nThen --------- = 5, and after mult. both sides by 3, we get 20-n = 15.              3Subtracting 15 from 20 results in 5 - n = 0, so we see that n = 5.