b Let g represented by the x-axis and q represented by the y-axis. Begin by determining the boundary line.
C
c Check whether the ordered pair (10,8) is in the shaded region.
A
a 3.45g+2.41q≤50
B
bGraph:
C
c No, the ordered pair (10,8) is not in the shaded region.
Practice makes perfect
a To write an inequality that represents the situation, we will organize the given information on a table. Notice that the total cost cannot exceed $50.
Verbal Expression
Algebraic Expression
Cost of g gallons of gas ($)
3.45 g
Cost of q quarts of oil ($)
2.41 q
The total cost must be less than or equal to $50
3.45 g+2.41 q≤50
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
&3.45g+2.41q ≤ 50 &&3.45g+2.41q = 50
Let g represented by the x-axis and q represented by the y-axis. We will draw the line by finding its intercepts. Let's first find its x-intercept (g-intercept) by substituting 0 for q.
Thus, the y-intercept is about 20.75. 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 gallons and quarts 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.
