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:
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 = [tex]2x+3y[/tex]
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.
[tex]2x+3y\leq 6[/tex]
The related equation is
[tex]2x+3y=6[/tex]
Substitute x=0 in the above equation.
[tex]2(0)+3y=6[/tex]
[tex]3y=6[/tex]
[tex]y=2[/tex]
The y-intercept is 2.
Substitute y=0 in the above equation.
[tex]2x+3(0)=6[/tex]
[tex]2x=6[/tex]
[tex]x=3[/tex]
The x-intercept is 3.
Check the inequality by (0,0).
[tex]2(0)+3(0)\leq 6[/tex]
[tex]0\leq 6[/tex]
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.
