# How To Graph Linear Equations

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```					                 How To Graph Linear Equations
How To Graph Linear Equations

We are going to learn about graphing linear equations in this unit. In order to solve the pair of
linear equations, we have an objective of getting the values of two unknown variables in the
equations, which satisfies both the equations.

These values can be a single pair of values, sometimes it is more than one value and in some
situations, we come across the pair of linear equations, which do not have any pair of
solutions. Solving the equations graphically I the best of all methods to get the solutions.

It is not very difficult task, but we say that graphing of equations require           skills and
understanding both.

One should be very careful while plotting the points on the graph and a special care for the
neatness of drawing the graph must be taken.

Analyzing the graph after drawing it is another important point to be taken care of. We must
know all the situations and possible outputs before the analysis of the equations plotted on
the graph is done. Let us learn this skill here in this unit.

Know More About :- How to Calculate Speed

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In order to get the solution for the pair of linear equations by "graphing linear equations", we
need to understand the concept of graphing the linear equations on the graph paper.

So for this we need to plot the table for the different values of and their corresponding values
of Y. We will put different values of x in the first equation and then for different values of x,
we get the different values of y.

In this way we get different set of point to represent the equation. On the graph paper, we will
plot the points and thus the equation will be represented graphically. Now in the same
manner, we will now represent the equation by plotting the points.

After the two equations are plotted on the graph paper, now we have to find the solution to
the given equation and thus we will predict the type of solution it is. There are different types
of results expected from the graph. They are :

1. If the two lines plotted to represent the two equations intersect at only one point, then we
conclude that the lines are intersecting and the solution to the pair of the equations is the
coordinates of the point where the two lines intersect each other.

2. If the two lines we have plotted on the graph do not intersect each other, then we say that
the pair of equations have no solution. In this case, we also come to the conclusion that the
pair of equations are parallel to each other.

3. If we have two equations such that the when we plot them on the graph, we get all the
points of the two equations as intersecting points, then we say that the pair of equations have
infinite number of solutions and all the points of the two lines intersect each other.

Thus we come to the conclusion that the two lines are coincident and the two equations
represent the same line. In such situations, we observe that the lines of the equations overlap
each other.

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How to graph linear equations Of y = mx + c

Step1: Choose the convenient values of x and find the corresponding values of y

Step 2: Prepare a table for different pairs of values of x and y

Step 3: Draw the axes on a graph paper and chose a suitable sale.

Step 4: Plot the ordered pairs fro the above table on the graph paper

Step 5: Join these points by a straight line This straight line is the graph of y = mx + c

Remark : In the equation y = mx + c, we say that

(i) m is the slope of the line

(ii) c is the y = intercept of the line.

Example : How to Graph Linear Equations of the line y = 2x + 3. Write down its

(i) y-intercept

(ii) slope.

Solution : We have x = 1

→ y = (2 x 1 = 3) = 5 x = - 2

→ y = {2 x (-2) + 3} = - 1

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