Write an inequality that represents
the fact that while making each item, you can’t exceed this limit. Be sure to
include the cost per item in this inequality.
c. Graph your inequality. Be sure to label your graph and shade the appropriate
side of the line.
d. Choose a point that falls in the shaded region. Explain what the x-coordinate
and y-coordinate represent and the significance in terms of cost of this point
falling in the shaded region.
e. Choose a point that falls directly on the line. Explain what the x-coordinate
and y-coordinate represent and the significance in terms of cost of this point
falling directly on the line.
f. Choose a point that does not fall in the shaded region. Explain what the xcoordinate and y-coordinate represent and the significance in terms of cost of
this point falling outside of the shaded region.
The inequality is:
Cost of each item ≤ limit
Let's assume the cost of each item is represented by the variable "x" and the limit is represented by the variable "L".
Therefore, the inequality can be represented as:
x ≤ L
To graph this inequality, we will plot a horizontal line on the x-axis at the value of L. Since the cost per item cannot exceed the limit, we shade the area to the left of the line.
A point that falls in the shaded region could be (4, 10). Here, the x-coordinate represents the cost of each item, which is $4, and the y-coordinate represents the limit, which is $10. This point falling in the shaded region signifies that the cost of each item is less than or equal to the limit, which is within the acceptable range.
A point that falls directly on the line could be (8, 8). Here, the x-coordinate represents the cost of each item, which is $8, and the y-coordinate represents the limit, which is also $8. This point falling directly on the line signifies that the cost of each item is equal to the limit, which is the maximum acceptable amount.
A point that does not fall in the shaded region could be (12, 6). Here, the x-coordinate represents the cost of each item, which is $12, and the y-coordinate represents the limit, which is $6. This point falling outside of the shaded region signifies that the cost of each item exceeds the limit, which is not within the acceptable range.