Question

Find the equation of the line which is parallel to X-axis and at a distance of 3units below the origin .​

Answer 1

Answer:

$x + 3 = 0$

Step-by-step explanation:

$y = 0 \: for \: line \: parallel \: to \: x - axis$

$equation \: of \: line \: is \: \\ x = - 3 \\ x + 3 = 0$

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that the required line be $l$ and slope of line $l$ be m

As it is given that, line $l$ is parallel to x - axis.

We know, $\boxed{ \rm{ \:slope\:of\:a\:line\:parallel\:to\:x - axis\:is\:0}}$.

$\rm\implies \:m \: = \: 0$

Further, given that line $l$ is at a distance of 3 units below the origin.

$\rm\implies \:$ Line $l$ passes through the point (0, - 3).

Now, we have line $l$ passes through the point (- 3, 0) and having slope, m = 0.

We know,

Slope point form of a line : - Equation of line which passes through the point $\rm \: (x_1, y_1)$ and having slope m is given by

$\boxed{ \rm{ \:y - y_{1} = m(x - x_{1}) \: }}$

So, here

$\rm \: x_{1} \: = \: 0$

$\rm \: y_{1} \: = \: - \: 3$

$\rm \: m \: = \: 0$

So, on substituting the values, we get

$\rm \: y - ( - 3) = 0(x - 0)$

$\rm\implies \:y + 3 = 0 \: \: or \: \: y = - 3$

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Short Cut Trick :- Equation of line $l$ which passes through the point (h, k) and parallel to x - axis is given by $\boxed{ \rm{ \:y = k}}$

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Additional Information :-

Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

Equation of line parallel to y - axis passes through the point (a, b) is x = a.

Equation of line parallel to x - axis passes through the point (a, b) is y = b.

2. Point-slope form equation of line

Equation of line passing through the point (a, b) having slope m is y - b = m(x - a)

3. Slope-intercept form equation of line

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

4. Intercept Form of Line

Equation of line which makes an intercept of a and b units on x - axis and y - axis respectively is x/a + y/b = 1.

5. Normal form of Line

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle β with the positive X-axis is x cosβ + y sinβ = p.