To understand the equation of a line perpendicular to x-axis, let us consider the figure given below.
In the figure above, clearly the line L is perpendicular to x-axis and passing through the value 'c' on x- axis.
So, the equation of a line perpendicular to x axis is
x = c
Note :
If the line is passing through some other value on x axis, we have to replace 'c' by that value.
Apart from the equation of a line which is perpendicular to x axis, let us look at some other different forms of equation of straight line.
The different forms of equation of straight line are,
(i) Slope intercept form
(ii) Point slope form
(iii) Two point form
(iv) Intercept form
Let us look at the above different forms of equation of straight line in detail.
Equation of a line in slope-intercept form is
y = mx + b
where m is the slope and b is the y-intercept.
Equation of a line in point-slope-intercept form
y - y_{1} = m(x - x_{1})
where m is the slope and (x_{1}, y_{1}) is a point on the line.
(x_{1}, y_{1}) and (x_{2}, y_{2}) are the two points on the line.
where a is the x-intercept and b is the y-intercept.
Apart from the above forms of equation of straight line, there are some other ways to get equation of a straight line.
1. If a straight line is passing through a point (0, k) on y-axis and parallel to x-axis, then the equation of the straight line is y = k.
2. Equation of x-axis is y = 0.
(Because, the value of y in all the points on x-axis is zero)
3. Equation of y-axis is x = 0.
(Because, the value of x in all the points on y-axis is zero)
4. Equation of a line in general form :
ax + by + c = 0
4. Equation of a line in standard form :
ax + by = c
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