[4 marks sum]

Question 14 Marks

Draw a graph for each of the following equations and find the coordinates of the points where the line drawn meets the $x-$axis and $y-$axis: $2x + 3y = 12$

Answer

$2 x+3 y=12$
$ \Rightarrow 3 y=12-2 x$
$ \Rightarrow y=4-\frac{2}{3} x$
When $x=3, y=4-\frac{2}{3}(3)=2$
When $x=-3, y=4-\frac{2}{3}(-3)=6$
When $x=6, y=4-\frac{2}{3}(6)=0$

$x$	$3$	$-3$	$6$
$y$	$2$	$6$	$0$

Plotting the points $(3, 2), (-3, 6)$ and $(6, 0),$ we get a line segment as shown in the figure.

The line meets the $x-$axis at $(6, 0)$ and $y-$axis at $(0, 4).$

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Question 24 Marks

Draw a graph of each of the following equations: $2(x-5)=\frac{3}{4}(y-1)$

Answer

$2(x-5)=\frac{3}{4}(y-1)$
$ \Rightarrow 8(x-5)=3(y-1)$
$ \Rightarrow 8 x-40=3 y-3$
$ \Rightarrow 3 y=8 x-40+3$
$ \Rightarrow 3 y=8 x-37$
$ y=\frac{8 x-37}{3}$
When $x =2,=\frac{8(2)-37}{3}=-7$
When $x=5, y=\frac{8(5)-37}{3}=1$
When $x=-1, y=\frac{8(-1)-37}{3}=-15$

$x$	$2$	$5$	$-1$
$y$	$-7$	$1$	$-15$

Plotting the points $(2, -7), (5, 1)$ and $(-1, -15),$ we get a line $AB$ as shown in the figure.

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Question 34 Marks

Draw a graph of each of the following equations:$=\frac{5}{2} \times+\frac{2}{5}$

Answer

$y=\frac{5}{2} x+\frac{2}{5}$
When $x=1, y=\frac{5}{2}(1)+\frac{2}{5}=2.9$
When $x=0, y=\frac{5}{2}(0)+\frac{2}{5}=0.4$
When $x=2, y=\frac{5}{2}(2)+\frac{2}{5}=5.4$

$x$	$1$	$0$	$2$
$y$	$2.9$	$0.4$	$5.4$

Plotting the points $(1, 2, 9), (0, 0.4)$ and $(2, 5.4),$ we get a line $AB$ as shown in the figure.

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Question 44 Marks

Draw a graph of each of the following equations: $x = -3y$

Answer

$x = -3y$
When $y = 1, x = -3(1) = -3$
When $y = 0, x = -3(0) = 0$
When $y = -2, x = -3(-2) = 6$

$x$	$-3$	$0$	$6$
$y$	$1$	$0$	$-2$

Plotting the points $(-3, 1), (0, 0)$ and $(6, -2),$ we get a line $AB$ as shown in the figure.

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Question 54 Marks

Draw a graph of each of the following equations: $x + y - 3 = 0$

Answer

$x + y - 3 = 0$
$\Rightarrow y = 3 - x$
When $x = 2, y = 3 2 = 1$
When $x = 0, y = 3 - 0 = 3$
When $x = 6, = 3 - 6 = - 3$

$x$	$2$	$0$	$6$
$y$	$1$	$3$	$-3$

Plotting the points $(2, 1), (0, 3)$ and $(6, -3),$ we get a line $AB$ as shown in the figure.

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Question 64 Marks

Draw a graph of each of the following equations: $5x + 2y = 16$

Answer

$5 x+2 y=16$
$ \Rightarrow 2 y=16-5 x$
$ \Rightarrow y=\frac{16-5 x}{2}$
When $x =2, y =\frac{16-5(2)}{2}=3$
When $x=4, y=\frac{16-5(4)}{2}=-2$
When $x=6, y=\frac{16-5(6)}{2}=-7$

$x$	$2$	$4$	$6$
$y$	$3$	$-2$	$-7$

Plotting the points $(2, 3), (4, -2)$ and $(6, -7)$, we get a line $AB$ as shown in the figure.

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Question 74 Marks

Draw a graph of each of the following equations:$ 3y + 2x = 11$

Answer

$3 y+2 x=11$
$ \Rightarrow 3 y=11-2 x$
$ \Rightarrow y=\frac{11-2 x}{3}$
When $x=1, y=\frac{11-2(1)}{3}=3$
When $x=-2, y=\frac{11-2(-2)}{3}=5$
When $x=-5, y=y=\frac{11-2(-5)}{3}=7$

$x$	$1$	$-2$	$-5$
$y$	$3$	$5$	$7$

Plotting the points$ (1, 3), (-2, 5)$ and $(-5, 7)$, w get a line $AB$ as shown in the figure.

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Question 84 Marks

Draw a graph of each of the following equations:$ 3x - 2y = 6$

Answer

$3 x-2 y=6$
$ \Rightarrow 2 y=3 x-6$
$ \Rightarrow y=\frac{3 x-6}{2}$
when $x=2, y=\frac{3(2)-6}{2}=0$
when $x=4, y=\frac{3(4)^2-6}{2}=3$
when $x=2, y=y=\frac{3(-2)-6}{2}=-6$

$x$	$2$	$4$	$-2$
$y$	$0$	$3$	$-6$

Plotting the point $(2, 0), (4, 3)$ and $(-2, -6),$ we get a line $AB$ as shown in the figure.

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Question 94 Marks

Draw a graph of each of the following equations: $x + 6y = 15$

Answer

$x + 6y = 15$
$\Rightarrow x = 15 - 6y$
When $y = 1, x = 15 - 6(1) = 9$
When $y =2, x = 15 - 6(2) = 3$
When $y = 3, x = 15 - 6(3) = -3$

$x$	$9$	$3$	$-3$
$y$	$1$	$2$	$3$

Plotting the points $(9, 1), (3, 2)$ and $(-3, 3),$ we get the line segment as shown in the figure.

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MATHEMATICS [4 marks sum]

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