Write out these two paragraphs about farming in Ghana using the right verb form as necessary:_ Trends in…

Question

Write out these two paragraphs about farming in Ghana using the right verb form as necessary:_ Trends in farming. In Ghana, the population of cities and towns (1) (grow) all the time. Because of this, and because cocoa prices (2) (fall) regularly, many farmers in Ghana (3) (turn) away from cocoa and (4) (go) into food production. On the whole, farmers (5) (seem) more (6) (interest) in (7) (grow) crops than in developing livestock. This (8) (mean) that there (9) (be) many opportunities for farmers to (10) (go) into good quality livestock farming. Usually, they (11) (start) off with a few goats and chickens, and gradually (12) (expand) into cattle or pigs. A farmer who (13) (follow) this route must be careful to observe the highest possible standards. Animals (14) (need) to be looked after carefully, and no one (15) (want) poor quality meat or dairy products.

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Focal Area 3: Graphs of Linear Functions - Analysis and Interpretation

(continued)
\begin{tikzpicture}[scale=0.7] \draw[->] (-3,0) -- (3,0) node[right] {$x$}; \draw[->] (0,-1) -- (0,6) node[above] {$y$}; \foreach \x in {-2,-1,1,2} \draw (\x,0) node[below] {$\x$} -- (\x,0.1); \foreach \y in {1,2,3,4,5} \draw (0,\y) node[left] {$\y$} -- (0.1,\y); % Graph of y = x + 3 (m=1) \draw[blue, thick] (-2, 1) -- (2, 5) node[above right] {$y=x+3$}; \fill[blue] (0,3) circle (2pt); % Graph of y = 2x + 3 (m=2) \draw[green, thick] (-2, -1) -- (2, 7) node[above right] {$y=2x+3$}; \fill[green] (0,3) circle (2pt); % Graph of y = -x + 3 (m=-1) \draw[red, thick] (-2, 5) -- (2, 1) node[below right] {$y=-x+3$}; \fill[red] (0,3) circle (2pt); \end{tikzpicture}
Explanation of how the gradient affects the steepness and direction of the line:
- The magnitude of the gradient ( $|m|$ ) determines the steepness of the line. A larger absolute value of $m$ means a steeper line. For example, $y = 2x + 3$ (with $|m|=2$ ) is steeper than $y = x + 3$ (with $|m|=1$ ).
- The sign of the gradient ( $m$ ) determines the direction of the line. A positive gradient (e.g., $m=1, m=2$ ) means the line slopes upward from left to right. A negative gradient (e.g., $m=-1$ ) means the line slopes downward from left to right.
A student observes that the graph of $y = 3x + 2$ passes through the points $(0, 2)$ and $(1, 5)$ .

Verify these points by substituting their coordinates into the equation.

*   For point $(0, 2)$:
    Substitute $x = 0$ and $y = 2$ into $y = 3x + 2$:
    $2 = 3(0) + 2$
    $2 = 0 + 2$
    $2 = 2$
    This is true, so the point $(0, 2)$ satisfies the equation.
*   For point $(1, 5)$:
    Substitute $x = 1$ and $y = 5$ into $y = 3x + 2$:
    $5 = 3(1) + 2$
    $5 = 3 + 2$
    $5 = 5$
    This is true, so the point $(1, 5)$ satisfies the equation.

Explain why they must satisfy the equation.

A point lies on the graph of an equation if and only if its coordinates satisfy the equation. This means that when the $x$-coordinate of the point is substituted into the equation, the resulting $y$-value must be equal to the $y$-coordinate of the point. Since both $(0, 2)$ and $(1, 5)$ yield true statements when substituted, they are indeed points on the line $y = 3x + 2$.

Analyze what would happen if a point did not satisfy the equation.

If a point did not satisfy the equation (e.g., if substituting its $x$-coordinate did not produce its $y$-coordinate), it would mean that the point **does not lie on the graph** of the function. For example, if we test the point $(2, 7)$ with $y = 3x + 2$: $7 = 3(2) + 2 \implies 7 = 6 + 2 \implies 7 = 8$, which is false. Therefore, $(2, 7)$ is not on the line $y = 3x + 2$.

Step-by-step solution

Verify these points by substituting their coordinates into the equation.

Explain why they must satisfy the equation.

Analyze what would happen if a point did not satisfy the equation.

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