## Question

Find the equation of the straight line which passes through the point (2, –3) and is

1. parallel to the x-axis

2. perpendicular to the x-axis

### Solution

–3, 2

1. Let equation of any line parallel to x-axis is

*y* = *b* … (i)

Since it passes through the point (2, –3).

Putting *y* = –3 in (i) then

*b* = –3

Hence required equation of the line is *y* = –3.

2. Let equation of any line perpendicular to x-axis = Equation of any line parallel to y-axis is

*x* = *a* … (ii)

Since it passes through the point (2, –3) putting *x* = 2 in (i)

Then 2 = *a* ⇒ *a* = 2

Hence the required equation of the line,

*x* = 2.

#### SIMILAR QUESTIONS

Find the slope of the line through the points (4, –6), (–2, –5).

Determine λ, so that 2 is the slope of the line through (2, 5) and (λ, 3).

Find whether the points (–*a*, –*b*), [–(*s *+ 1)*a*, –(*s* + 1)*b*] and [(*t* – 1)a, (*t* – 1)*b*] are collinear?

For what value of *k* the points (*k*, 2 – 2*k*), (–*k* + 1, 2*k*) and (–4 – *k*, 6 – 2*k*) are collinear?

Find the angle between the lines joining the points (0, 0), (2, 3) and (2, –2), (3, 5).

The angle between two lines is and the slope of one of them is . Find the slope of the other line.

A line passes through the points *A*(2, –3) and *B*(6, 3). Find the slopes of the lines which are

1. parallel to *AB*

2. perpendicular to *AB*

Find the equation of the straight line parallel to y-axis and at a distance

(i).3 units to the right

(ii). 2 units to the left

Find the equation of the straight line parallel to *x*-axis and at a distance

(i). 5 units above the *x*-axis

(ii). 9 units below the *x*-axis

Find the equation of a line which is equidistant from the lines .