[tex]\rm\implies \:y + 3 = 0 \: \: or \: \: y = - 3\\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Short Cut Trick :- Equation of line [tex] l [/tex] which passes through the point (h, k) and parallel to x - axis is given by [tex] \boxed{ \rm{ \:y = k}}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
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.
Answers & Comments
Answer:
[tex]x + 3 = 0[/tex]
Step-by-step explanation:
[tex]y = 0 \: for \: line \: parallel \: to \: x - axis[/tex]
[tex]equation \: of \: line \: is \: \\ x = - 3 \\ x + 3 = 0[/tex]
Verified answer
[tex]\large\underline{\sf{Solution-}}[/tex]
Let assume that the required line be [tex] l [/tex] and slope of line [tex] l [/tex] be m
As it is given that, line [tex] l [/tex] is parallel to x - axis.
We know, [tex]\boxed{ \rm{ \:slope\:of\:a\:line\:parallel\:to\:x - axis\:is\:0}} [/tex].
[tex]\rm\implies \:m \: = \: 0 \\ [/tex]
Further, given that line [tex] l [/tex] is at a distance of 3 units below the origin.
[tex]\rm\implies \: [/tex] Line [tex] l [/tex] passes through the point (0, - 3).
Now, we have line [tex] l [/tex] 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 [tex] \rm \: (x_1, y_1) [/tex] and having slope m is given by
[tex]\boxed{ \rm{ \:y - y_{1} = m(x - x_{1}) \: }} \\ [/tex]
So, here
[tex]\rm \: x_{1} \: = \: 0 \\ [/tex]
[tex]\rm \: y_{1} \: = \: - \: 3 \\ [/tex]
[tex]\rm \: m \: = \: 0 \\ [/tex]
So, on substituting the values, we get
[tex]\rm \: y - ( - 3) = 0(x - 0) \\ [/tex]
[tex]\rm\implies \:y + 3 = 0 \: \: or \: \: y = - 3\\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Short Cut Trick :- Equation of line [tex] l [/tex] which passes through the point (h, k) and parallel to x - axis is given by [tex] \boxed{ \rm{ \:y = k}}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
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.