To draw the solution set, begin by determining the boundary line of the inequality.
Inequality: 12x+3y≤ 60 Graph:
Practice makes perfect
We will start by writing the inequality that represents the situation. Then, we will draw the solution set.
Writing Inequality
Let x be the number of pizzas and y be the number pitchers of soft drinks. We can write total cost for pizza and soft drinks in terms of x and y.
Product
Cost ($)
Total Cost ($)
Pizza
12
12 x
Pitcher of soft drink
3
3 y
Since Coach Washington does not want to spend more than $ 60, we have the following inequality.
12 x+3 y ≤ 60
Drawing Solution Set
To draw the graph the solution set, we will first determine its boundary line. It can be determined by replacing the inequality symbol with the equals sign.
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&Inequality III &Boundary Line III
&12x+3y ≤ 60 &12x+3y = 60
The boundary line is in standard form. Therefore, it would be a better option to find its intercepts to graph it. We will substitute y= 0 for the x-intercept and x= 0 for the y-intercept.
12x+3y=60
Operation
x-intercept
y-intercept
Substitution
12x+3( 0) = 60
12( 0)+3y = 60
Calculation
x=5
y=20
Point
(5,0)
(0,20)
Now we can plot the intercepts and connect them with a line segment. Notice that the number of pizzas and pitchers of soft drink cannot be negative, so the line will be bound by the axes. The boundary line will also be solid because of the non-strict inequality.
Next, we will decide which region we should shade by testing the point (0,0).
