A farmer harvests maize from his land. The relation between the acres of land cultivated (x) and the bags of maize harvested (y) is given by y = 3x + 9. The farmer cultivates between 1 and 9 acres. a)

For $x=1$: $y = 3(1) + 9 = 12$
For $x=2$: $y = 3(2) + 9 = 15$
For $x=3$: $y = 3(3) + 9 = 18$
For $x=4$: $y = 3(4) + 9 = 21$
For $x=5$: $y = 3(5) + 9 = 24$
For $x=6$: $y = 3(6) + 9 = 27$
For $x=7$: $y = 3(7) + 9 = 30$
For $x=8$: $y = 3(8) + 9 = 33$
For $x=9$: $y = 3(9) + 9 = 36$

The table of values is:

$$\begin{array}{|c|c|} \hline x \text{ (acres)} & y \text{ (bags)} \\ \hline 1 & 12 \\ 2 & 15 \\ 3 & 18 \\ 4 & 21 \\ 5 & 24 \\ 6 & 27 \\ 7 & 30 \\ 8 & 33 \\ 9 & 36 \\ \hline \end{array}$$

b) Draw a graph that shows the relation between maize and land used
To draw the graph, plot the points $(x,y)$ from the table above.
The recommended scale is $2\text{cm}$ to represent $1\text{acre}$ on the x-axis and $2\text{cm}$ to represent $5\text{bags}$ of maize on the y-axis.
The points to plot are: $(1, 12), (2, 15), (3, 18), (4, 21), (5, 24), (6, 27), (7, 30), (8, 33), (9, 36)$.
Connect these points with a straight line.

c) Determine how many:

i) Bags of maize ($y$) can be harvested from 3.5 acres of land ($x$)

$$y = 10.5 + 9$$ $$y = 19.5$$

The farmer can harvest $\boxed{\text{19.5 bags}}$ of maize.

ii) Acres of land ($x$) are used to harvest 31 bags of maize ($y$)

$$31 - 9 = 3x$$ $$22 = 3x$$ $$x = \frac{22}{3}$$ $$x \approx 7.333$$

The farmer uses approximately $\boxed{\text{7.33 acres}}$ of land.

Item 2: Mountain Climb Translations

a) Help each group identify their new locations on the mountain.
The initial position for all groups is $(0,0)$. A translation $(a,b)$ moves a point $(x,y)$ to $(x+a, y+b)$.

• Group A: Initial position $(0,0)$, translation $T=(3,5)$. New location $A' = (0+3, 0+5) = \boxed{(3,5)}$.

• Group B: Initial position $(0,0)$, translation $M=(-2,7)$. New location $B' = (0+(-2), 0+7) = \boxed{(-2,7)}$.

• Group C: Initial position $(0,0)$, translation $N=(5,-8)$. New location $C' = (0+5, 0+(-8)) = \boxed{(5,-8)}$.

b) Illustrate on the same pair of axes the new locations of each group of learners
To illustrate, plot the following points on a coordinate plane:

• Group A: $(3,5)$
• Group B: $(-2,7)$
• Group C: $(5,-8)$