Q57. - Algebra 2

Question

SCRAPBOOK For exercise 56-58, use the following information.

Ian has $6.00, and he wants to buy paper for his scrapbook. A sheet of printed paper costs 30¢, and a sheet of solid color paper costs 15¢.

 

 57. Graph the inequality.

Step-by-Step Solution

Answer

The graph of the inequality $0.3x+0.15y\le 6$ is:

Step 1 - Observe the inequality symbol

Since the inequality symbol is $\le$, the graph of the related linear equation $0.3x+0.15y=6$ is solid. This will be the boundary of the inequality.

Step 2 - Test (0,0)

Note that point (0,0) is usually a good point to test since it is standard origin and leads to simpler calculations. Substitute 0 for x and 0 for y into the inequality $0.3x+0.15y\le 6$.

$\begin{array}{c}0.3\left(0\right)+0.15\left(0\right)\le 6\\ 0+0\le 6\\ 0\le 6\text{ True}\end{array}$

Therefore, shade the region that contains the point (0,0).

Step 3 - Graph the inequality

Shade the region that contains the point (0,0) and also, since the variables cannot be negative, shade only the part in the first quadrant as the number of sheets bought cannot be negative.