Question 1: Find the equation of the line parallel to x-axis and passing through $(3, 5)$

Equation of a line parallel to x-axis is $y = k$

The line passes through $( 3, -5)$

$\therefore k = -5$

Hence the equation of the line is $y + 5 = 0 \text{ or } y = - 5$

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Question 2: Find the equation of the line perpendicular to x-axis and having intercept $- 2$ on x-axis.

Equation of  a like perpendicular to x-axis is $x = k$

The line passes through $(-2, 0)$

$\therefore k = -2$

Hence the equation of line is $x + 2 = 0 \text{ or } x=-2$

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Question 3: Find the equation of the line parallel to x-axis and having intercept $-2$ on y-axis.

Equation of a line parallel to x-axis is $y = k$

The line passes through $( 0, -2)$

$\therefore k = -2$

Hence the equation of the line is $y + 2 = 0 \text{ or } y = -2$

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Question 4: Draw the lines $x=-3, x=2, y = -2, y =3$ and write the coordinates of the vertices of the square so formed.

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Question 5: Find the equations of the straight lines which pass through $(4, 3)$ and are respectively parallel and perpendicular to the x-axis.

i)        Equation of a line parallel to x-axis is $y = k$

The line passes through $( 4, 3)$

$\therefore k = 3$

Hence the equation of the line is $y -3 = 0 \text{ or } y = 3$

ii)      Equation of  a like perpendicular to x-axis is $x = k$

The line passes through $(4,3)$

$\therefore k = 4$

Hence the equation of line is $x -4 = 0 \text{ or } x = 4$

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Question 6: Find the equation of a line which is equidistant from the lines $x = - 2$ and $x = 6$.

Line equidistant from the lines $x = - 2$ and $x = 6$ will pass through the mid point of ( -2, 0) and ( 6, 0) which is (2,0)

Equation of  a like parallel to y-axis is $x = k$

The line passes through $(2,0)$

$\therefore k = 2$

Hence the equation of line is $x - 2 = 0 \text{ or } x=2$

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Question 7: Find the equation of a line equidistant from the lines $y = 10$ and $y = -2$.

Line equidistant from the lines $y = 10$ and $y = -2$ will pass through the mid point of $( 0,10)$ and $( 0, -2)$ which is $(0, 4)$
Equation of a line parallel to x-axis is $y = k$
The line passes through $( 0,4)$
$\therefore k = 4$
Hence the equation of the line is $y -4 = 0 \text{ or } y = 4$