A line passes through the origin and through points A(−2, b−14) and B(14−b, 72). What is the greatest possible value of b? PLS HELP!!! 80PTS

Step-by-step explanation:

If a line passes through A , B and O(0,0) the slopes of AO and BO or AO and OB should be same depending on ... What is the greatest possible value of b? ... (14 - b)^2 = 72*2 = 144 .

Since it passes through the origin, there is no y-intercept

and the equation has the form

y = mx

(−2, b−14) and B(14−b, 72)

slope = (72 - b + 14)/(14-b + 2) = (86-b)/(16-b)

the "critical values of" seem to be 86 and 16

If b > 86, the slope is positive

if b < 16, the slope is positive

for 16 < b < 86 the slope is negative

There doesn't seem to be a greatest value of b.

e.g. let b = 1000

then the slope is (86-1000)/(16-1000) = 457/492 = .9288..

and your equation is y = 457/492 x

as x ---> ∞ , slope > 1

first, let's see what the pattern is.

58 - x = 47

46 - x = 36

x = 9

so this means that the term after 25 is 25 - 9:

the next term in the sequence is 16.