1. if 9 students sharpen 18 pencils in 2 minutes, how many students will it take to sharpen 18 pencils in 1 minute? a.) 2 b.) 9 c.) 18 d.) 36 2. if y varies inversely with x, and y = –16 when x = –64, what is the constant of variation? a.) 16 b.) 64 c.) 100 d.) 1,024 3. the pair of points (3, 8) and (x, 6) are on the graph of an inverse variation. what is the missing value? a.) 4 b.) 3 c.) -1 d.) 1,

A) If 9 students sharpen 18 pencils in 2 minutes,Then if the time is halved, it will take twice as many men to sharpen 18 pencils.Hence it will take 18 students to sharpen 18 pencils in one minute B) y & 1/x. Then y = K/x where K is our constant of proportionality.Then K = yx. When x = -64 and y = -16 then K = -64 * -16 = 1024. Option DC) When x = 3 y = 8. So for an inverse variation K as calculated from B = 3 * 8 = 24.Then when K = 24 and y = 6; we have 24 = 6x. Hence x = 4. Option A

One solution:
y = ax + b from our given example we get the following system:

If we subtract first equation to the second we will get the following

4h - 2h = ah + b - (3ah+b) 
2h = ah +b - 3ah - b
2h = ah - 3ah + b - b
2h = ah - 3ah
2h = ah (1 - 3) = -2ah

If we divide both sides by 2h we will get

2h/2h = -2ah/2h     which is equal to the following:

1 = -1a    from here we can assume that a = -1

so ours slope is a = -1

Second solution:
We can use the formula of slope:
slope = 

slope = 

in our case 

So we will have the following:
slope =