a What is the inequality sign if the team needs to raise at least $2000?
B
b Start by graphing the boundary line. Is it solid or dashed?
C
c Choose points in the shaded region.
D
d Plot the points you chose in the graph.
A
a x+ 1.25y ≥ 2000
B
b
C
cExample Solution: (800,1200), (1000,1600), (1700,1400), (1400,800), and (500,1500).
D
dExample Graph:
Practice makes perfect
a Let x be the number of hot dogs and y the number of sodas the team sells. Note that the price of each hot dog is $1.00, and the price of each soda is $1.25. We can write an expression for the total earnings from these sales.
1 * x+ 1.25 * y ⇔ x+1.25y
The cost of the new goals is $2000. Therefore, our expression should be greater than or equal to 2000.
x+ 1.25y ≥ 2000
b To graph the inequality we will follow two steps.
To obtain the boundary line, we replace the inequality sign with an equals sign.
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Inequality & & Boundary Line [0.8em]
x+1.25y ≥ 2000 & & x+1.25y = 2000
To graph the boundary line, we will first write in it slope-intercept form.
We will now use the slope - 45 and the y-intercept 1600 to graph the line. Note that the inequality is not strict, so the boundary line will be solid. Since the number of items cannot be a negative number, the domain and range contain only non-negative numbers.
Region
To determine the region we should shade, we will test a point. If substituting the point into the inequality produces a true statement, we will shade the half-plane that contains the point. Otherwise, we will shade the opposite region. For simplicity, we will test the point (0,0).
