Linear Graph

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 y-intercept.


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

  1. Take any value for x.

  2. Substitute the value of x in the equation to find the value of y.

  3. Plot the x and y values on the graph.

  4. To plot another point repeat step 1.

  5. Join the two points and we get the straight line.


X and Y-Intercepts

  1. Set y=0 to find the x-intercept and solve for x.

  2. Set x=0 to find the y-intercept and solve for y.

  3. Now plot the x-intercept and the y-intercept on the graph.

  4. Join the two points and we get a straight line.


Slope-Intercept

  1. Plot the point after you find the y-intercept.

  2. Use the slope and find the another point and plot it using the y-intercept.

  3. Join the two points and we get a straight line.


Solved Examples

Example 1: Observe the graph given and write it in slope-intercept 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 slope-intercept 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 distance-time graph. With the help of the linear graph, calculate

  1. The time is taken by Rami to ride 100 km.

  2. 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 x-axis

FAQ (Frequently Asked Questions)

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 non-linear graph is not a straight line. A graph when plotted does not give a straight line then it is said to be a non-linear graph.

The general representation of nonlinear equations is;

ax2 + by2 = c

Where x and y are the variables and a,b and c are the constant values.

When a graph is plotted for non-linear equation we get a curve and its slope values changes.