The graph of y=b is a straight line : * parallel to x axis parallel to y axis passes through origin coincident on x axis
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Answer:
Step-by-step explanation:
Coordinate geometry is the branch of mathematics that deals with algebra and geometry. It is used to study geometric figures like parabolas and straight lines by using numbers.
There are mainly two axes in the geometry. One is horizontal (x-axis), and the other is vertical (y-axis). These two axes meet at the intersection point known as the origin.
The location of the point can be shown by using an ordered pair (x,y). Here
x-abscissa
y-ordinate
On the right side of the x-axis we have positive values, and on the left side, we have negative values. Similarly, on the upside of the y-axis, the values are positive, and bottom side, the values are negative.
Equations of Lines Parallel to X-axis and Y-axis:
A straight line has infinitely many solutions. The straight-line graph is obtained by joining some of the points (solutions) of the line in a cartesian plane. The graph of the line depends on the position of the point that represents the solution.
Sometimes the graph of the line passes through the origin, and sometimes it intersects the axes: x-axis, y-axis. And, sometimes, it is parallel to the axes: x-axis and the y-axis. The general form of the line parallel to x-axis for any real number k is in the form of y=k And in the equation y=k, the real number k gives the distance of the point (solution of the line) from the x-axis.
For example, the equation of the line, that is in the form of y=5, is a line parallel to the x-axis and passing through the point (0,5) on the y-axis. Here, the graph of the given linear equation y=5 describes that it is at a distance of 5 units from the x-axis.
The general form of the line parallel to y− axis for any real number k is in the form x=k. And in the equation x=k, the real number k gives the distance of the point (solution of the line) from the y-axis.
For example, the equation of the line, that is in the form of x=5, is a line parallel to the y-axis and passing through the point (5,0) on the x-axis. Here, the graph of the given linear equation x=5 describes that it is at a distance of 5 units from the y-axis.
Equation of a Line Parallel to X-axis
We can write the equation of the line parallel to x-axis in generalised form as in the form of y=k(k∈R), where k be any real-valued number.
Here, in the equation of the line parallel to x-axis, which is in the form of y=k, the real number k gives the distance of the line from the x-axis. The line parallel to the x-axis lies either above or below the x-axis.
The equation of the line y=k, lies parallel to x-axis at a k units distance from above the x-axis.
The equation of the line y=−k, lies parallel to x-axis at a k units distance from below the x-axis.