Line Graph Definition
What is linear? Linear means a straight line. And what is a graph? A graph is a pictorial representation of our data in an organized manner. So we can say that a graph when plotted gives a single straight line then it is said to be a linear graph.
Linear relationships are used in our day to day life. These relationships can be expressed in many different ways. Linear graphs, when graphed they give a straight line. Linear graphs can be sketched or plotted on graph paper.
Line Graph Definition
When a set of data varies with time, we usually use a line graph to represent them. In a line graph, the data are usually plotted against time and each pair of adjacent data points is joined by a straight line segment. The main advantage of using a line graph to represent data is that we can observe the trend of the movement of data. Hence, we may use a line graph to forecast certain future data values.
Now it is clear that what is linear, we can define it as,
Sometimes, the graph is a single straight line. Such a graph is called a linear graph.
To draw a linear graph, we need to locate some points on the graph paper. Join these points. If the line joining these points is a straight line, then it is a linear graph.
Linear Graph Equation
A linear equation or an equation of a straight line.
General Form

ax + by + c = 0, where a, b, c are constants.
Slope Intercept Form

y = mx + b, where m is the gradient or the slope and b is the yintercept.
Point Slope Form

y – y1 = m (x – x1), where m is the gradient or slope and x1 and y1 are coordinates of a given point.
Linear Diagram
A linear diagram can be represented as follows:
How to graph a linear equation?
We can plot a graph by three methods they are:
Plot Points
 Take any value for x.
 Substitute the value of x in the equation to find the value of y.
 Plot the x and y values on the graph.
 To plot another point repeat step 1.
 Join the two points and we get the straight line.
X and YIntercepts
 Set y=0 to find the xintercept and solve for x.
 Set x=0 to find the yintercept and solve for y.
 Now plot the xintercept and the yintercept on the graph.
 Join the two points and we get a straight line.
SlopeIntercept
 Plot the point after you find the yintercept.
 Use the slope and find the another point and plot it using the yintercept.
 Join the two points and we get a straight line.
Solved Examples
Example 1: Observe the graph given and write it in slopeintercept form i.e y = mx + b.
Solution:
Given
The slope is 1
The y intercept is 1
Substitute this into y=mx+b
we get y = x – 1
So the equation is y = x 1
Example 2: Find the equation of the straight line that has slope m = 2 and passes through the point (–1, –4).
Solution: By the slopeintercept form we have;
y=mx+c
Given,
m=2
we have;
y = 4 and x = 1
Substitute the values in the above equation, we get
4 = 2(1) + c
4 = 2 + c
c = 4 – 2 = 6
Hence, the required equation will be;
y = 2x – 6
Quiz Time:
1. Ram can ride a honda constantly at a speed of 40 km/hour. Draw a distancetime graph. With the help of the linear graph, calculate

The time is taken by Rami to ride 100 km.

The distance covered by Ram in 5 hours.
2. Draw the line passing through A(2,5) andExample 1 B(4, 5). Find the coordinates of the point at which this line meets the xaxis
1. What is the meaning of Linear in Math?
The word linear comes from the Latin word ‘linearis’ which means belonging to a line. Linear means a straight line. Mathematically linearity is a property of representing the data graphically whose output is a straight line. Something is said to be linear if it is in a straight line.
On a cartesian plane, a linear function is a function where the graph is a straight line. A simple linear function can be represented as y = a + bx which plotted on the graph traces a straight line. When the value of x is increased y gradually increases.
It is represented as
2. What is Non – Linear Graph?
As the name implies nonlinear graph is not a straight line. A graph when plotted does not give a straight line then it is said to be a nonlinear graph.
The general representation of nonlinear equations is;
ax^{2} + by^{2} = c
Where x and y are the variables and a,b and c are the constant values.
When a graph is plotted for nonlinear equation we get a curve and its slope values changes.