Question 1: Draw the graph of each of the following linear equations:

(i) $x=0$     (i) $y=0$     (iii) $x+4=0$     (iv) $x-3=0$     (v) $y +2=0$

(vi) $y -7 = 0$     (vii) $2y-3=0$     (viii) $3x+7 =0$     (ix) $y=x$     (x) $y=-x$

(xi) $y = 2x$     (xii) $y=-3x$     (xiii) $2y + 3x = 0$     (xiv) $5y - 2x = 0$

(xv) $y =2x+5$     (xvi) $x+y+1=0$     (xvii) $x-y+4=0$

(xviii) $2x + 3y - 12 = 0$     (xix) $3x + 4y +24=0$     (xx) $2x-3y +6=0$

i) to viii)

ix) to xii)

xiii) to xvi)

xvii) to xx)

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Question 2: Find the slope and y-intercept of the lines represented by each of the following equations:     (i) $4x-3y+8=0$    (ii) $2x+y-5=0$              (iii) $5y+4=0$   (iv) $y = 2x$    (v) $2x-3y =0$

For finding the slope and y-intercept, convert the equation into the form $y = mx + c$

i) $4x-3y+8=0$

$\Rightarrow 3y = 4x + 8$

$\Rightarrow y =$ $\frac{4}{3}$ $x +$ $\frac{8}{3}$

$\therefore slope (m) =$ $\frac{4}{3}$  and  $y-intercept =$ $\frac{8}{3}$

(ii) $2x+y-5=0$

$\Rightarrow y = -2x + 5$

$\therefore slope (m) = -2$  and  $y-intercept = 5$

(iii) $5y+4=0$

$\Rightarrow y = (0) x +$ $\frac{-4}{5}$

$\therefore slope (m) = 0$  and  $y-intercept =$ $\frac{-4}{5}$

(iv) $y = 2x$

$\therefore slope (m) = 2$  and  $y-intercept = 0$

(v) $2x-3y =0$ $$\Rightarrow 3y = 2x$ $\Rightarrow y =$ $\frac{2}{3}$ $x + 0$ $\therefore slope (m) =$ $\frac{2}{3}$ and $y-intercept = 0$ $\\$ Question 3: Draw the graph of the line represented by the equation $3x - 2y + 6 = 0$. Also, find the coordinates of the points where the line meets with the coordinate axes. Answer: To draw the line $3x - 2y + 6 = 0$  x 0 -2 y 3 0 $\\$ Question 4: Draw the graphs of the lines represented by each of the following equations: $2x+3y=12$, $x-y=1$ Find the coordinates of the vertices of the triangle formed by the two lines and the y-axis. Answer: To draw the line$latex $2x+3y=12$

 x 0 6 y 4 0

To draw the line \$latex $x-y=1$

 x 0 1 y -1 0

Vertices of the triangle are $(0, -1), (3, 2) \ \& \ (0, 4)$

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Question 5: Draw the graphs of the following pairs of lines on the same graph paper and find their points of intersection. Are these lines perpendicular to each other?     (i) $x - y + 4 = 0$, $x + y - 6 = 0$                        (ii) $x + 2y - 6 = 0$,   $2x-y + 8 =0$

i)

To draw the line $x - y + 4 = 0$

 x 0 -4 y 4 0

To draw the line $x + y - 6 = 0$

 x 0 6 y 6 0

Intersection is $(1, 5)$. They are perpendicular (from the graph we can see that). Also the slope of the first line is $1$ while the slope of the second line is $-1$. We know if the product of the two slopes is $-1$ (which is the case here) the lines are perpendicular.

ii)

To draw the line $x + 2y - 6 = 0$

 x 0 6 y 3 0

To draw the line $2x-y + 8 =0$

 x 0 4 y 8 0

Intersection is $(-2, 4)$. They are perpendicular (from the graph we can see that). Also the slope of the first line is $-$ $(\frac{1}{2})$ while the slope of the second line is $2$. We know if the product of the two slopes is $-1$ (which is the case here) the lines are perpendicular.

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Question 6: Draw the graph of the following pairs of lines on the same graph paper and hence check whether they are parallel or not:

(i) $y=3x+2$,   $y=3x-4$    (ii) $2x+y-5=0$,    $x-2y +7 =0$                          (iii) $3x+2y- 8 = 0$,    $3x+2y +12= 0$

(i) $y=3x+2$,   $y=3x-4$

To draw the line $y=3x+2$

 x 0 -(2/3) y 2 0

To draw the line $y=3x-4$

 x 0 (4/3) y -4 0

The lines on the graph are parallel. Slope of first line is $3$ while the slow of the second line is also $3$. This also proves that the lines are parallel as the slopes of the lines are equal.

(ii) $2x+y-5=0$,    $x-2y +7 =0$

To draw the line $2x+y-5=0$

 x 0 2.5 y 5 0

To draw the line $x-2y +7 =0$

 x 0 -7 y 3.5 0

The lines on the graph are not parallel. Slope of first line is $-2$ while the slow of the second line is also $-\frac{1}{2}$. This also proves that the lines are parallel as the slopes of the lines are not equal.

(iii) $3x+2y- 8 = 0$,    $3x+2y +72= 0$

To draw the line $3x+2y- 8 = 0$

 x 0 (8/3) y 4 0

To draw the line $3x+2y +12= 0$

 x 0 -4 y -6 0

The lines on the graph are parallel. Slope of first line is $-(3/2)$ while the slow of the second line is also $-(3/2)$. This also proves that the lines are parallel as the slopes of the lines are equal.

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