Parallel To The Y Axis

Lines Parallel to Axes

In ii-dimensional geometry, at that place are two axes, which are the x-axis and the y-centrality. A line that is parallel to the y-axis is of the form 'x=m', where '1000' is whatsoever real number and 'one thousand' is the distance of the line from the y-axis. For case, the equation of a line which is of the form x = iii is a line parallel to the y-axis and is 3 units away from the y-centrality. Similarly, lines can exist drawn parallel to the ten-axis also. A line that is parallel to the 10-axis is of the grade 'y=k', where 'chiliad' is a real number and is as well the distance of the line from the x-axis. For case, the equation of a line which is of the form y = two is a line that is parallel to the x-axis and is 2 units away from the x-axis.

1.	Line Parallel to x-axis
2.	Line Parallel to y-axis
iii.	Solved Examples
4.	Practice Questions
5.	FAQs on Lines Parallel to Axes

Line Parallel to x-axis

A line that is parallel to the x-axis is of the course 'y = k', where 'k' is a abiding value. In a coordinate airplane , a directly line can be represented by an equation. To put the equation of this parallel line in a more than generalized form, nosotros can write it as 'y = k', where 'm' is whatever existent number . Besides, 'k' is said to exist the altitude from the x-centrality to the line 'y=thousand'. For case, if the equation of a line is y = five, and then nosotros can say that it is at a distance of v units above the x-centrality line. All the points on a line that is parallel to the ten-axis are at the same altitude away from it.

Consider the equation y = ii, or y - ii = 0. This is an equation with a single variable y. Nonetheless, we can retrieve of information technology as a two-variable linear equation in which the coefficient of x is 0:

0(x) + i(y) + (-two) = 0.

Let us plot the graph for the equation, and discover how the line 'y=2' volition expect.

x	-4	-3	-2	-1	0	i	2	iii	4
y	2	2	2	2	two	2	2	2	two

Substituting every value of 'x' given in the table, we encounter that the value of 'y' remains unchanged. For case, let us accept the value of 'x = -iv' and substitute in the equation, 0(x) + ane(y) + (-ii) = 0.
0(-four) + i(y) - two = 0
0 + y - ii = 0
Therefore, y = ii.
Allow u.s.a. take a positive value for 'x = 3' and solve the equation to find the value of 'y'.
0(iii) + 1 (y) - 2 = 0
0 + y - 2 = 0
y = ii.
Therefore, nosotros tin see that though the value of 'x' changes, the value of 'y' remains unchanged. Thus, all solutions of this linear equation are of the grade (grand,2), where k is some real number. The graph of the line 'y=2' is given below.

Line Parallel to x-axis

This is a line parallel to the ten-axis. Thus, an equation of the form y = a represents a straight line parallel to the x-axis and intersecting the y-axis at (0,a).

Line Parallel to y-centrality

A line that is parallel to the y-centrality is x = thou, where 'k' is a constant value. This means that for whatever value of 'y', the value of 'x' is the same. A more than generalized manner to correspond an equation of a direct line parallel to the y-axis is x = chiliad, where 'k' is a real number. Here, 'g' represents the distance from the y-axis to the line 'ten=k'. For instance, if we have the equation of a line as 'x =2', information technology says that the line is at a altitude of 2 units away from the y-axis. All the points on a line that is parallel to the y-axis are at the same distance away from it.

Now, consider the equation ten = 3. This can also be written as a two-variable linear equation, equally follows:

i(10) + 0(y) + (-3) = 0.

Let us plot the graph for the equation, and find how the line 'ten=3' will look.

x	three	3	3	3	three	3	iii	three	3
y	-4	-3	-2	-1	0	ane	2	3	4

Substituting different values of 'y' in the equation, i(x) + 0(y) + (-three) = 0, the value of 'x' remains unchanged. For example, if y = -3, so the value of 'x' is,
i(x) + 0(-iii) +(-3) = 0.
x + 0 - iii = 0
x -3 = 0
Therefore, x = 3.
Let us take a positive value for 'y'. Say 'y=2'. On substituting the value of 'y=two', we get,
1(ten) + 0(2) + (-3) = 0
10 + 0 -3 =0
Therefore, x = iii.
We can detect that for any value of 'y', the value of x = 3. Thus, the solutions of this equation are all of the course (3,k), where k is some real number. The graph of this equation will consist of all points whose x-coordinate is 3, that is, a line parallel to the y-centrality, and passing through (3,0). The graph of the line whose equation is x = 3 is shown in the figure below.

Line Parallel to y-axis

In general, an equation of form x = a represents a straight line parallel to the y-axis and intersecting the x-axis at (a,0).

Topics Related to Lines Parallel to Axes

Cheque out some interesting manufactures related to lines parallel to axes. Click to know more!

Lines
x and y-axis
Coordinate Axes
Cartesian Coordinates
Equation of a Directly Line

Example i: What does the equation 2x + 3 = - 1 stand for when considered every bit a linear equation in 2 variables?

Solution:When considered as a linear equation in two variables, this represents a line parallel to the y-axis, as shown below.

Taking the equation 2x + 3 = -1, and solving for x, nosotros go,
2x+3 = -1
2x = -1 -iii
2x = -4
x = -four/2
10 = -ii
Therefore, the equation 2x + iii = -1 represents a line that is parallel to the y-axis, which is x = -2. The line ten = -two is shown in the effigy beneath.
Case 2: The following figure shows four lines, each of which is parallel to one of the two axes. Determine the equation of each line.

Solution: \(L_{one}\) is parallel to the ten-axis and passes through (0, 2). Thus, the equation of \({L_1}\) will be y = 2. \({L_2}\) is parallel to the y-centrality and passes through (-1, 0). The equation of \({L_2}\) will exist x = -one.

Similarly, the equation of \({L_3}\) will exist \(y = - \frac{3}{2}\) and that of \({L_4}\) will be \(x = \frac{v}{ii}\).

go to slidego to slide

Breakup tough concepts through elementary visuals.

Math will no longer be a tough bailiwick, particularly when you sympathize the concepts through visualizations.

Book a Free Trial Form

FAQs on Lines Parallel to Axes

What Does Parallel to the Axes Hateful?

Parallel to axes means the lines that are parallel to either the x-axis or y-axis. A line parallel to the 10-axis is a horizontal line whose equation is of the form y = thou, where 'k' is the distance of the line from the x-axis. Similarly, a line parallel to the y-axis is a vertical line whose equation is of the class x = k, where 'grand' is the altitude of the line from the y-centrality.

What is the Equation of the Line Parallel to x-axis?

The equation of the 10-axis is given by y = 0. The equation of the line parallel to the ten-axis is y = thou, where 'yard' is any existent number. For example, because the equation of a line, y = ii, for any value of '10' the value of 'y' is always equal to 2. This can be understood by substituting various values of 'ten' in the line equation, 0(x) + i(y) - 2 = 0, which always results in y =ii. This line is parallel to the x-axis.

What is the Equation of the Line Parallel to y-axis?

The equation of the y-centrality is given by x = 0. The equation of the line parallel to the y-axis is ten = k, where 'one thousand' is any real number. For example, considering the equation of a line, x = 3, for whatever value of 'y' the value of 'x' is always equal to 3. This can be understood by substituting various values of 'y' in the line equation, 1(x) + 0(y) - 3 = 0, which e'er results in x = 3. This line is parallel to the y-axis.

When Can You lot Say That Two Lines are Parallel to the Axes?

All the vertical and horizontal lines on a plane are parallel to the axes. Horizontal lines are parallel to the x-axis while vertical lines are parallel to the y-axis. A line is parallel to axes if either the 10-coordinate or y-coordinate is fixed or constant throughout the line and information technology should pass from either (0, a) or (a, 0). For instance, a line with the equation, 3x - half-dozen = 0 is parallel to y-centrality, since for any value of 'y' the value of ten remains the aforementioned, which is 2. Similarly, the line with the equation 4y - 8 = 0 is parallel to the x-axis, since, for any value of 'x', the value of 'y' remains the same, which is ii.

What is the Equation of Line Parallel to y-centrality and Passing Through (3, iv)?

The equation of the line parallel to the y-axis takes the class of 10 = k. The coordinate (3.iv) lies on the equation of the line to exist found. Therefore, substituting the value of 'x' in the equation 'x = grand' , nosotros go iii = k or grand = 3. Therefore the equation of the line parallel to the y-axis passing through (three.4) is 'x = 3'.