Find the equations of the straight lines which pass through (4, 3) and

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

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

Answer»

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.