Question

(05.05) Nethan made 8 rose bouquets and 6 daffodil bouquets. Nethan only has enough flowers to make at most 20 rose or daffodil bouquets total. Let x represent the number of more rose bouquets and y represent the number of more daffodil bouquets that Nethan can make. Which of the following graphs best represents the relationship between x and y? (4 points) line joining ordered pair 0, 20 and 10, 10 and the region below this line which lies in the first quadrant is shaded. line joining ordered pair negative 2, 6 and 4, negative 2 and the region below this line which lies in the first quadrant is shaded. line joining ordered pair negative 4, 10 and 6, 0 and the region below this line which lies in the first quadrant is shaded. line joining ordered pair negative 6, 8 and 8, negative 10 and the region below this line which lies in the first quadrant is shaded.

Answer 1

The answer for this question is C

Answer 2

Number of bouquets of rose possessed by Nethan = 8

Number of bouquets of daffodil possessed by Nethan=6

Also , there is a statement regarding rose and daffodil bouquets.

Nethan only has enough flowers to make at most 20 rose or daffodil bouquets total.

1.  → x +y ≤ 20

Equation of line joining two points (a,b) and (p,q) is given by:

$\frac{y-b}{x-a}=\frac{q-b}{p-a}$

Starting from option

1. line joining ordered pair (0, 20) and (10, 10) and the region below this line which lies in the first quadrant is shaded.

→ $\frac{y-20}{x-0}=\frac{20-10}{0-10}\\\\y-20= -x \\\\ x+ y=20$

2.line joining ordered pair  (-2, 6) and (4, - 2) and the region below this line which lies in the first quadrant is shaded

→ $\frac{y-6}{x+2}=\frac{6+2}{-4-2}\\\\-3 y+18= 4 x+8 \\\\ 4 x+3 y-10=0$

3. line joining ordered pair  (-4, 10) and (6, 0) and the region below this line which lies in the first quadrant is shaded.

→ $\frac{y-10}{x+4}=\frac{10-0}{-4-6}\\\\y-10= -x -4 \\\\ x+ y-6=0$

4. line joining ordered pair (- 6, 8) and (8,  -10) and the region below this line which lies in the first quadrant is shaded.

→ $\frac{y-8}{x+6}=\frac{-10-8}{8+6}\\\\7 y-56= -9 x -54 \\\\ 9 x+7 y-2=0$

Option 1, line joining ordered pair (0, 20) and (10, 10) and the region below this line which lies in the first quadrant is shaded is correct option describing the relationship between at most 20 rose or daffodil bouquets total that nethan can make from remaining flowers.