Question

A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an

Answer 1

Answer:

The first graph represents how many of each order could be put in a bag hanging from the hook ⇒ 1st

Step-by-step explanation:

* Lets explain how to solve the problem

- The order of jumbo paperclips weighs 2 pounds

- x is the number of orders of paperclips

∴ The weight of the paperclips order is 2 × x = 2x

- The order of packing tape weighs 3 pounds

- y is the number of orders of packing  tape

∴ The weight of the tape order is 3 × y = 3y

- The weight of the total order is 2x + 3y

- The hook can hold no more than 6 pounds

∴ 2x + 3y ≤ 6

- Lets find the graph which represent this inequality

∵ The equation of any line is y = mx + c, where m is the slope of the

  line and c is the y-intercept

- The y-intercept means substitute x in the equation by 0

- The x- intercept means substitute y in the equation by 0

∵ The inequality is 2x - 3y ≤ 6

∵ The equation of the line is 2x + 3y = 6

- Subtract 2x from both sides

∴ 3y = 6 - 2x

- Divide both sides by 3

∴ y = 6/3 - 2/3 x

∴ y = 2 - 2/3 x

- Find the y-intercept

∵ x = 0

∴ y = 2

∴ The line intersect the y-axis at point (0 , 2)

- Find the x-intercept

∵ y = 0

∴ 0 = 2 - 2/3 x

- Add 2/3 x to both sides

∴ 2/3 x = 2

- Multiply both sides by 3

∴ 2 x = 6 ⇒ divide both sides by 2

∴ x = 3

∴ The line intersect the x-axis at point (3 , 0)

- From the figure the first and the second figures have the same

 x-intercept and y-intercept

∵ The inequality is 2x + 3y ≤ 6

- The sign ≤ means the line is sold and the shading is under the line

∴ The first figure is the answer

* The first graph represents how many of each order could be put in a

  bag hanging from the hook

Answer 2

Answer:

Option A.

Step-by-step explanation:

Let x is the number of orders of paperclips and y is the number of orders of packing tape.

An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds.

Total weight = $2x+3y$

A hook in an office storage closet can hold no more than 6 pounds. It means total weight must be less than or equal to 6 pounds.

$2x+3y\leq 6$

The related equation is

$2x+3y=6$

Substitute x=0 in the above equation.

$2(0)+3y=6$

$3y=6$

$y=2$

The y-intercept is 2.

Substitute y=0 in the above equation.

$2x+3(0)=6$

$2x=6$

$x=3$

The x-intercept is 3.

Check the inequality by (0,0).

$2(0)+3(0)\leq 6$

$0\leq 6$

This statement is true, it means (0,0) is included in the shaded region.

The sign of inequity is "≤" it means the related line is a solid line and shaded region lie below the line.

Therefore, the correct option is A.