Linear graph is represented in the form of a straight line. To show a relationship between two or more quantities we use a graphical form of representation. If the graph of any relation gives a single straight line then it is known as a linear graph. The word "linear" stands for a straight line. The linear graph is a straight line graph that is drawn on a plane connecting the points plotted on x and y coordinates.
|1.||Linear Graph Definition|
|2.||Linear Graph vs Line Graph|
|3.||Linear Graph Equation|
|4.||FAQs on Linear Graph|
Linear Graph Definition
"A linear graph is the graphical representation of a straight line." It showcases a linear equation in two variables and shows the linear association between two quantities.
Let's understand with the help of an example.
James was offered a job where he would be paid $15 per hour. He has an average daily expenditure of $50. He wants to know, how many minimum hours he should work in a day so that he has some savings. Let's study how a linear graph can answer this problem.
If we represent time by t and income by I, we get a linear equation: I =15t
With the help of the above plotted linear graph, we can analyze that the value on the vertical axis is more than his expenditure of $50.
The value on the horizontal axis gives the minimum number of hours James should work to have some savings every day.
According to the graph if he will work 5 hours daily then he can manage his earnings up to $ 75($15 × 5 hours = $ 75) and he can have savings $(75 - 50) of $ 25.
Linear Graph vs Line Graph
Let's understand the difference between a linear graph and a line graph with help of an image.
In the figure given above, can you make out how B is different from A?
Here, A is a linear graph whereas B represents a line graph.
Though both of them are made up of line segments, there is a major difference between them.
But in the case of a line graph, they may or may not be collinear.
Linear Graph Equation
A linear graph is the graphical representation of a linear equation.
A linear equation is an equation that can be written in the form: Ax + By = C, for some real numbers A, B, and C where A and B, are not 0.
For example, the linear equation 2x + 5y = 0 on a graph looks like this:
How To Plot Linear Equation On a Graph?
Consider the following steps to plot a linear equation on a graph:
- step1: Identify the two quantities which are varying.
- step2: Let the 1st quantity be x and the 2nd quantity is y.
- step3: Next, find out three ordered pairs (x, y) which satisfy the given equation.
- step4: Present these values in a tabular form.
- step5: Plot the points given in the table on a cartesian plane.
- step6: Join the points.
For example, 2x + y = 6
To plot this on a graph we write it in the form y = mx + b
So, y =−2x + 6
To get the solution to the linear equation, we can plug in a numerical value to x and obtain the corresponding value for it.
Three of the solutions are:
Now, plot these points on an XY plane and join them.
- To plot a linear graph, two pairs of (x,y) are sufficient. But, we won't come to know if there is a mistake in obtaining these values as two points can always be joined and they represent a line. It is advised to plot one more point to ensure that the solutions obtained for the given linear equation are correct.
- The equation y = kx (where k is a real number) represents a line parallel to X-axis i.e. horizontal line.
- The equation x = ky (where k is a real number) represents a line parallel to Y-axis i.e. vertical line.
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Check out these interesting articles to know more about the linear graph and its related topics.
Linear Graph Examples
Example 1: Mrs. Mariot asks John to identify that the given equation 3x - 7y = 16 forms a linear graph or not without plotting its values. Help John to identify whether it is a linear graph or not.
Solution: The equation 3x - 7y = 16 is a linear equation in two variables. That's the 1st thing John needs to observe.
Next, he needs to recall that any linear equation in two variables always represents a straight line.
These two pieces of information are sufficient to tell about the nature of the graph.
Thus, the given equation represents a linear graph.
Example 2: Mike has to prepare a linear graph for the equation 2x + y = 8. Complete the table given below for this equation.
x __ 4 -2 y 8 __ __
Case 1: y = 8, x = ?
2x + y = 8
2x + 8 = 8
2x = 8−8 = 0
x = 0
Case 2: x = 4, y = ?
2x + y = 8
2 × 4 + y = 8
8 + y = 8
y = 0
Case 3: x =−2,y = ?
2x + y = 8
2 × (−2) + y = 8
−4 + y = 8
y = 8 + 4 =12
The solutions are :
x 0 4 -2 y 8 0 12
FAQs on Linear Graph
What is the Difference Between the Line and the Linear Graph?
Even though both line graphs and linear graphs are made up of line segments, there is a major difference between them.
How do you Know a Graph is Linear Graph?
When a linear equation shows a straight line on a graph, we can say that the graph is a linear graph. The linear graph is a graph with a straight line.
What is the Difference Between a Linear Graph and a Non-Linear Graph?
The equation of a linear graph such as 3x + 4y =6, forms a straight line, whereas the non-linear graph has graphs with a curved line. In a non-linear graph, if we coordinate the equation such as x2 + y2 = 2, we will not get a straight line.
What are Linear Graphs Used For?
Linear graphs help to predict future values. Linear graphs are used for different purposes like checking the rate of change of income, production, temperature, etc. over a given time period.
How does a Linear Graph Look Like?
Consider a linear equation, y = mx + b. When we draw a linear graph, its slope(i.e the value of m) is always a constant number. A constant slope denotes a straight line. Hence, a linear graph looks like a straight line.
Does a Linear Graph have to go Through the Origin?
NO, a linear Graph does not have to go through the origin. No need to pass through the origin. This relation is linear, that's why the graph is showing a straight line.
How do you Find the Equation of a Linear Graph?
If the graph of a line is given, we can determine the equation in two ways. First is slope-intercept form, y = mx+b. The second is point-slope form, y - y1 = m (x - x1). The slope and one point on the line is required to write the equation of a line.