Question

A painting crew bought 30 gal of paint for a job. The crew members used 3 gal of paint per hour until they used all the paint.

Which sketch represents this situation?



A) A graph in the first quadrant containing a line segment. The x axis is labeled Hours and the y axis is labeled Gallons remaining. The endpoints of the line segment are begin ordered pair 0 comma 3 end ordered pair and begin ordered pair 30 comma 0 end ordered pair.


B) A graph in the first quadrant containing a line segment. The x axis is labeled Hours and the y axis is labeled Gallons remaining. The endpoints of the line segment are begin ordered pair 0 comma 30 end ordered pair and begin ordered pair 10 comma 0 end ordered pair.


C) A graph in the first quadrant containing a line segment. The x axis is labeled Hours and the y axis is labeled Gallons remaining. The endpoints of the line segment are begin ordered pair 0 comma 10 end ordered pair and begin ordered pair 30 comma 0 end ordered pair.


D)A graph in the first quadrant containing a line segment. The x axis is labeled Hours and the y axis is labeled Gallons remaining. The endpoints of the line segment are begin ordered pair 0 comma 30 end ordered pair and begin ordered pair 3 comma 0 end ordered pair.

Answer 1

The answer to this question is A.)

Answer 2

Explanation:

They have 30 gallons of paint and for each hour that passes, they use 3 gallons of paint. Therefore, we can express that as a function:

y = -3x + 30

where y = gallons left

and x = hours passed

Therefore, the end points are (0, 30) and (10, 0)

Using our function when 0 hours has passed:

y = -3(0) + 30

y = 30

Therefore one endpoint is when x = 0 y = 30 or (0,30)

Using our function when 10 hours has passed:

y = -3(10) + 30

y = -30 + 30

y = 0

Therefore one endpoint is when x = 10 y = 0 or (10, 0)

The graph can be seen in the picture below.