Question

Tom has $10 that he wants to use to buy pens and pencils. However, he does not want to buy more pens than pencils. A pen costs $3, and a pencil costs $1. Which graph represents this scenario?

Answer 1

number of pencils x

number of pens y

3x + y = 10
x ≤ y

Draw the line 3x + y = 10 .[it passes by (0,10) and (-10/3,0)

Draw the line y=x [it passes by (0,0), (1,1), (2,2) etc]

Then the solution is the points with integer x and y, that belong to the segment of the line 3x +y = 10 between the x-axis and the line y=x. Those points are (1,7) , (2,4), (3, 1).