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

The equation of the line parallel to the x-axis is y = b.

It is given that y = b passes through (4, 3).

∴ 3 = b
$\Rightarrow$ b = 3

Thus, the equation of the line parallel to the x-axis and passing through (4, 3) is y = 3.

Similarly, the equation of the line perpendicular to the x-axis is x = a.

It is given that x = a passes through (4, 3).

∴ 4 = a
$\Rightarrow$ a = 4

Thus, the equation of the line perpendicular to the x-axis and passing through (4, 3) is x = 4.

Hence, the required lines are x = 4 and y = 3.