Answer:
- <u>the first graph:</u> line passing through the points (3, 0) and (0,2), and the shaded region is below the line.
Explanation:
<u>1) Find the expression that represents the situation.</u>
The expression that represents the situation is an inequality:
- Number of orders of paper clips: x
- Weight of an order of paper clips: 2 lbs
- Total weight of x orders of paper clips: 2x
- Number of orders of packing tape: y
- Weight of an order of packing tape: 3 lbs
- Total weight of y orders of packing tape: 3y
- Total weight of paper clips and packing tape in a bag: 2x + 3y
- Maximum weight hold by the hook: 6 lbs
Hence, the total weight must be less than or equal to (≤) 6 lbs, which is:
- 2x + 3y ≤ 6
<u>2) Graph of the inequality 2x + 3y ≤ 6</u>
Line:
- Border line: 2x + 3y = 6
- x-intercept: y = 0 ⇒ 2x = 6 ⇒ x = 6 /2 ⇒ x = 3 ⇒ point (3,0)
- y-intercept: x = 0 ⇒ 3y = 6 ⇒ y = 6 /3 ⇒ y = 2 ⇒ point (0,2)
Shaded region:
- Symbol ≤ means that the line is included, which is represented with a solid line, and the region is below the line.
Conclusion: the graph is the line passing through the points (3, 0) and (0,2), and the shaded region is below the line, so that is the first graph of the picture.
Note: strictly speaking, you should include the restrictions that the variables x and y cannot be negative, with which the graph would be only on the first quadrant but those constrains are not handled in the problem.
The graph is also attached.
