Question

In a paint factory, an old conveyer line has filled 10 barrels of paint, and is filling more at a rate of 2 barrels per minute. A worker just switched on a newer line that can fill 3 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How many barrels will each line have filled?

Simplify and put into Slope-Intercept form

Answer 1

see below

Explanation:

First line:

y = mx+b where m is the slope and b is the y intercept

y = 2x + 10

Second line

y = mx+b

y = 3x+0 since there are no barrels filled on this line when they flip the switch

Setting the two equations equal

2x+10 = 3x

Subtract 2x from each side

2x+10-2x= 3x-2x

10 = x

Each line will have filled 10 barrels when they numbers are equal.