Applications of Linear Graph

In today's life, we see many changes in which the value of distant quantities depend on changes in the values of other quantities. For example,if the number of families visiting a restaurant increases, the income of the restaurant increases and, vice versa, if the Indian population is employed or unemployed, the time taken to finish a task decreases or increases. Hence, in some situations, the value of one quantity increases with the decrease in the value of another quantity whereas in some situations the value of one quantity decreases with an increase in the value of another quantity. Hence, two quantities are either included in direct proportion or indirect proportion. The relationship between these two quantities or the applications of linear graphs can be described in an arithmetic way or graphical way (using graphs). Sometimes these two quantities show a linear dependence, in other words, changes in the value of one quantity is proportional to the first power of variation in the value of another quantity. We usually describe these linear graph applications through linear graphs.


In this article, we will discuss linear graph applications, real life applications of straight line graph, linear application and graph etc.


What is a Linear Graph

The linear graph is a straight graph or straight line which is drawn on a plane and intersecting points on x and y coordinates. Linear equations are used in everyday life and a straight line is formed graphing those relations in a plane. These linear graph applications are described through linear graphs.


Linear Graph Equation

As we know, the linear graph form a straight line and represent the following equation

y = ax+b

In the above equation, 'a' represents the gradient of the graph and 'b' in the graph represent y-intercept.

The gradient between any two points (x₁, y₁) and (x₂, y₂) are any two points drawn on the linear or straight line.

The value of gradient a is defined as the ratio of the difference between the  y-coordinates and the x-coordinates.

a = (y₂-y₁) /(x₂ - x₁)

Or y-y₁= a (x – x₁)

The linear equation can also be written as,

Ax + by + c= 0

Linear Applications and Graph

The given situation  below shows linear applications and graphs to describe the situation.


Sonia can drive a two-wheeler continuously  at a speed of 20 km/hour. Construct a distance-time graph for this situation. Through the linear graph, calculate

  1. The time taken by Sonia to ride 100 km.

  2. The total distance covered by Sonia in 3 hours.

Solution: Now, we will construct a graph with the help of the above values given in the table.

Let us now construct a table that represents distance traveled and time taken by Sonia to cover the total distance of 100 km in the particular time-interval.


Time(hr)

1

2

3

4

5

6

Distance(km)

20

40

60

80

100

120


Let us now draw a graph with the help of the values given above in the tabulated form.


(image will be uploaded soon)


Through the above linear application and graph graph, we can calculate the required values,

  1. Time taken by Sonia to cover 100 km

In the above linear graph 

X-coordinate of the graph corresponding to the Y-coordinate of the graph at 100 = 5.

Hence, time taken by Sonia to cover 100 km is 5 hours.

  1. The total distance covered by Sonia in 3 hours

In the above linear graph,

Y-coordinate of the graph corresponding to the X-coordinate of the graph at 3 = 60.

Hence, the total distance covered by Sonia in 3 hours = 60 km.


Real-Life Applications of Straight-Line Graph

Some of the real-life applications of the straight line graph are given below:

  1. Future contract markets and opportunities can be described through straight line graphs.

  2. Straight line graph used in medicine and pharmacy to figure out the accurate strength of drugs.

  3. Straight line graphs are used in the research process and the preparation of the government budget.

  4. Straight line graphs are used in Chemistry and Biology.

  5. Straight line graphs are used to estimate whether our body weight is appropriate according to our height.


Solved Examples

1. Plot the below coordinates on the graph and answer the following questions.

(2, 210), (5, 420), (7, 560), (6, 490), (3, 280), (1, 140), (8, 630)

1. Is the graph drawn from the above coordinates represent a linear graph?

2. Find the value of x-coordinate if y-coordinate corresponds to 350?

3. Calculate the value of y-coordinate for which x-coordinate is 11, If the graph drawn is linear.


Solution: 

The graph for the above coordinates is shown below

(image will be uploaded soon)

  1. The graph drawn is linear.

  2. The x and y coordinates will be (4,350).

  3. The value of y coordinate or which x-coordinate is 11 will be 840. The x and y coordinates will be (11, 840).


2. A security job pays \[\$20\] per hour. A graph of income depending on hours worked is drawn  below. With the help of the graph shown below, determine how many hours are needed to earn \[\$60\].

(image will be uploaded soon)


Solution: By determining \[\$60\] amount on the vertical axis which represents income in dollars in graph, you can follow a horizontal line ( represent time in hour) through the value, until it meets the graph. Follow a vertical line straight down from there, until it meets the horizontal axis. Hence, the value in hours is 3. It implies that the 3 hours of work is needed to earn \[\$60\].


Quiz Time

1. The important attributes in the graphical representation of the straight line are

  1. X-intercept

  2. Y-intercept

  3. a- intercept

  4. Both a and b


2. What will be the y-intercept of the ordered pair (8,6) of the linear equation?

  1. -6

  2. 6

  3. -8

  4. 8

FAQ (Frequently Asked Questions)

1. Explain the linear Function.

The linear function is defined as a function that draws a straight line in a graph. It is primarily a polynomial function whose degree is approximately 1 or 0. Each term of the linear function is either a constant or the product of a constant and (the first power of) a single variable. For example, a common function y = ax +b (also known as slope-intercept) is represented as a linear function because it satisfies both the conditions with x and y as variables and a and b as constants. It is linear as the exponent of the x term is a one (first power), and it follows the definition of a function, for each input (x) there is exactly one output (y).

2. Explain the Nonlinear Function.

In Economics,a linear function does not explain the relationship between variables. In such a condition a nonlinear function must be used. The graph of a nonlinear function does not form a straight line whereas it represents curved lines in a graph. A curved line is defined as a line whose direction changes repeatedly. The slope of a nonlinear function is distinct at each point on the line. Some examples of nonlinear functions are exponential function, parabolic function, inverse functions, quadratic function, etc. All these functions do not meet the condition of the linear equation y = ax + b. The expression of all these functions are distinct.