Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x–axis.
Given, A line which is perpendicular and parallel to x–axis respectively and passing through (4, 3)
To Find: Find the equation of that line.
Formula used: The equation of line is [y – y1 = m(x – x1)]
Explanation:
Case 1 : When Line is parallel to x–axis
So, The parallel lines have equal slopes,
And, the slope of x–axis is always 0, then
The slope of line, m = 0
Coordinates of line are (x1, y1) = (4, 3)
The equation of line is y – y1 = m(x – x1) – – – – (1)
By putting the values in equation (1), we get
y – (3) = 0(x – 4)
y – 3 = 0
Case 2: when line is perpendicular to x–axis
Here, The line is perpendicular to the x–axis, then x is 0 and y is – 1.
So, The slope of the line is, m =
m =
Coordinates of line are (x1, y1) = (4, 3)
The equation of line = y – y1 = m(x – x1)
By putting the values, we get
x = 4
Hence, The equation of line when it is parallel to x –axis is y = 3 and it is perpendicular is x = 4.