Question

Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x–axis.

Answer 1

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 = \(\frac{y}{x}\)

m = \(\frac{-1}{0}\) 

Coordinates of line are (x₁, y₁) = (4, 3) 

The equation of line = y – y₁ = m(x – x₁) 

By putting the values, we get

y - 3 = \(\frac{-1}{0}(x-4)\) 

x = 4 

Hence, The equation of line when it is parallel to x –axis is y = 3 and it is perpendicular is x = 4.