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)

By using the formula,

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

Let us consider,

Case 1: When Line is parallel to x–axis

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)

Now substitute the values, we get

y – (3) = 0(x – 4)

y – 3 = 0

Case 2: When line is perpendicular to x–axis

The line is perpendicular to the x–axis, then x is 0 and y is – 1.

The slope of the line is, m = y/x

= -1/0

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

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

Now substitute the values, we get

y – 3 = (-1/0) (x – 4)
x = 4

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