Linear Graph - Visualizing Data

Linear means straight and a graph is a diagram which shows a connection or relation between two or more quantity. So, the linear graph is nothing but a straight line or straight graph which is drawn on a plane connecting to points on x and y coordinates. We use linear relations in our everyday life and by graphing those relations in a plane, we get a straight line.

Now that you have got an introduction to the linear graph, let us explain it more through its definition and an example problem.

Linear Graph Definition

As discussed, linear graph forms a straight line and denoted always as an equation;

\(y=mx+c\)

where m is the gradient of the graph and c is the y-intercept of the graph.

The gradient between any two points (\(x_{1},y_{1}\)) and (\(x_{2},y_{2}\)) are any two points on the linear or straight line.

The value of gradient m is ratio of the difference of y-coordinates and the difference of x-coordinates.

i.e.

\(m=y_{2}-y_{1}/x_{2}-x_{1}\)

Or

\(y-y_{1}= m (x – x_{1})\)

The linear equation can also be written as,

\(ax + by + c = 0\)

where a,b and c are constants

Linear Graph Examples

Let us understand the Linear graph definition with examples.

  1. The equation \(y=2x+1\) is a linear equation or forms a straight line on the graph. When the value of x increases then ultimately the value of y also increases by twice of the value of x plus 1.
  2. Suppose, if we have to plot a graph of a linear equation \(y=2x+1\).

Let us consider \(y=2x+1\) forms a straight line. Now, first we need to find the coordinates of x and y by constructing below the table;

x

-2

-1

0

1

2

y

Now calculating value of y with respect to x, by using given linear equation,

\(y=2x+1\)

\(y=2(-2)+1\)= -3 for \(x=-2\)

\(y=2(-1)+1\)= -1 for \(x=-1\)

\(y=2(0)+1\)= 1 for \(x=0\)

\(y=2(1)+1\)= 3 for \(x=1\)

\(y=2(2)+1\)= 5 for \(x=2\)

So the table can be re-written as;

x

-2

-1

0

1

2

y

-3

-1

1

3

5

Now based on these coordinates we can plot the graph as shown below.

Linear Graph

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Practise This Question

In a game of football, if a player kicks the ball into opponent's goal post then he scores a goal. If he passes the ball to any of his team mates and that particular team mate scores a goal after that, the player is said to have assisted the goal. Here you have line graphs which give the goals and assists of two players in past 5 months. The player who played better in Month 5 is ________. (Assume the level of competition in the matches played by both the players was same)