Answer:
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.
