c Check whether the ordered pair (50,50) is in the shaded region.
A
a 8x+6y≤700
B
bGraph:
C
c Yes, the ordered pair (50,50) is in the shaded region.
Practice makes perfect
a To write an equation that represents the situation, we will organize the given information on a table. Let x be the number of hours Carlos works at Main St. Deli. Let y be the number of hours Carlos works babysitting. Remember that at least means that greater than or equal to.
Verbal Expression
Algebraic Expression
Earning from working x hours at Main St. Deli ($)
8 x
Earning from y hours babysitting ($)
6 y
The total earning must be at least $700
8 x+6 y≥700
b We can graph the inequality by finding its boundary line. It can be found by replacing the inequality symbol with the equals sign.
&Inequality &&Boundary Line
&8x+6y ≥ 700 &&8x+6y = 700
Next, we will determine the intercepts of the line. Let's first find its x-intercept by substituting 0 for y.
Thus, the y-intercept is about 116.7. We will plot these points and connect them with a line segment. The line will be solid because the inequality is non-strict. Since the number of hours cannot be negative, the line will be bound by the axes.
In the final step, we will test an arbitrary point to decide which region we should shade. We will test the point (0,0) to make the math bit easier.
