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### How to graph the equation of a line?

Graphing an equation is easy. To graph the equation of a line, you have to obtain the points through which the line passes. Then plot the points on the graph sheet, and then join the points to obtain the equation of the line.

How to obtain the points through which a line passes?

Take the given equation, and plug in at least 3 random values for x in the equation. For example, in the equation 4x + 3y = 0, we can plug in
x = 0, x = 1, x = -1, x = -2, x = 2, or any other value for x.

Then for each value of x, find the corresponding value of y. For example, if you plug in x = 0 in the equation 4x + 3y = 0, you get
4(0) + 3y = 0
3y = 0
y = 0

Therefore the corresponding values for x and y are 0 and 0 respectively. This means that the line passes through the point (x, y), that is, (0, 0).

Similarly, plug in a number of (at least three) different values for x in the given equation, and obtain the points in the form of (x, y) for each value of x.
Now you have to plot the points on the graph sheet.

How to plot the points obtained above?

For the coordinates of any point (x, y), the 'x' coordinate represents the value on the x axis and the 'y' coordinate represents the value on the y axis.

The x axis is the horizontal axis, and the y axis is the vertical axis.

Now to plot a point, mark its 'x' coordinate on the x axis and 'y' coordinate on the y axis. Now draw perpendicular lines from these two points to the axes. These two perpendicular lines will meet at a point. This is the point that is represented by (x, y).

Example of plotting points: Plot the point (1, 3) on the coordinate plane.

Step 1: Take a graph sheet, and draw the x and y axis on it.
Step 2: The x coordinate of the point (1, 3) is x = 1. So mark the point on the x axis where the value is 1.
Step 3: The y coordinate of the point (1, 3) is y = 3. So mark the point on the y axis where the value is 3.
Step 4: Now draw perpendicular lines from the above two marks to their respective axes.
Step 5: Mark the point where these two perpendicular lines meet. This is the point (1, 3)

Joining the points to make the graph:

Now to make the graph of the given equation, you simply have to join all the points plotted in the above step by a line.
If the points do not come in a straight line, then probably there is some mistake in plotting these points, or in calculating the x and y coordinates of these points. So first check whether they are plotted correctly, and if so, then check the calculation of the point.