Lots of points!

malachi took cans to the recycling plant and put them into the can-crusher one at a time. after he had already crushed some of the cans, he started recording the number of cans he crushed per minute. the table shows how many cans malachi put in the can-crusher at different times.

minutes: 3 i 5 l 7 l 9
cans crushed: 49 l 65 l 81 l 97

what is the equation that represents malachi’s situation? record any fractional answers in decimal form. (y – 65) = (x – ) (fill in the blanks)

If y represents the total number of cans already crushed at a given time, 
and x represents the number of minutes, 
then we can observe that this is a point-slope equation for the point (5,65). 

The point-slope format is 
y - b = m (x - a) 
where m is the slope of the line 
and (a,b) are coordinates of a point on the line. 

Since we're given b=65, we find the x-coordinate that corresponds to 65 on the table, 
and therefore we know a=5. 

We also need to fill in the blank for the slope. It turns out the slope is constant for the whole table, so we can use any two points to calculate it. Using the endpoints (3,49) and (9,97), we get 
m = (difference in y-coordinates) / (difference in x-coordinates) 
= (97 - 49) / (9 - 3) = 48/6 = 8 

So now we know that a=5, b=65, m=8 and the point-slope equation 
y - b = m (x - a) 
turns out to be 
y - 65 = 8 (x - 5)