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# Line Graph

In geometry, we study about lines, angles and shapes. A line is the one-dimensional figure. It has no breadth and height. A segment of the line is known as line segment. A line segment is the distance between two points. A line is represented by a linear equation. A linear equation is an equation which has a degree of one. We can say that an equation which has highest variable exponent as one. A linear equation shows a straight line which has no curves in between.

Line graph is a special graph that is very commonly used in statistics. If the relation involving any two measures can be symbolized by means of a straight line in a graph then such graphs are known as linear graphs. A line graph is also known as linear graph. It represents a straight line on the graph. An algebraic equation in which every term is moreover a constant or the product of a constant and a single variable is said to be linear equation. The linear equation is an equation of the form y = mx + c, where m is referred to the slope of the equation and c is its Y intercept. In the equation y = mx + c, when we substitute each value of x, it provides a significance of y, we acquire an ordered pair (x, y) of numerals.

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## What is a Line Graph?

A line graph is a graph that uses points and lines to show change over time. A line graph is a diagram that shows a line joining several points, or a line that shows the relationship between the points. Graph displays quantitative information between two changing variables with a line or curve that connects a series of successive data points.Line graphs compare two variables. Each variable is plotted along an axis. A line graph has a vertical axis and a horizontal axis.

## Line Graph Data

Data to create data tables and line graphs following the particular way for making a line graph. If we have already created data tables, then we make line graphs using the data tables. Line graphs are plotted as a series of points, which are then joined with straight lines and provide a simple way to review data collected over time. Line graph provides an excellent visual format of the outcome data collected over time.

In the line graph, the points and lines are drawn on a grid in order to show change over a time period.

## Parts of a Line Graph

Various parts of the line graph:

Title: The title is explains what the graph is about.

Scale: The scale is the numbers that show the units used on the line graph.

Labels: Both the side and the bottom of the line graph have a label that tells what kind of data is shown. X-axis describe what each data point on the line represents and y-axis shows the numeric value for each point on the line.

Bars:
The bar measures the data number.

Data values: Data values are the actual numbers for each data point.

## Make a Line Graph

Steps to Make a Line Graph:

Step 1: Use the data from the table to choose an appropriate scale.

Step 2: Draw and label the scale on the vertical and horizontal axis.

Step 3: List the each item and locate the points on the graph.

Step 4: Connect the points with line segments.

You can see a line plotted through two points say A and B on the graph below. Click and drag the points to change the line graph.

## Types of Line Graphs

Line graph have one or more lines plotted on the graph. They are very useful for showing change over time.

Type of line graphs include:

1. Simple Line Graph: Only one line is plotted on the graph.

2. Multiple Line Graph: More than one line is plotted on the same set of axes. A multiple line graph can effectively compare similar items over the same period of time

3. Compound Line Graph:
If information can be subdivided into two or more types of data. This type of line graph is called a compound line graph. Lines are drawn to show the component part of a total. The top line shows the total and line below shows part of the total. The distance between each two lines shows the size of each part.

### Vertical Line Graph

Vertical line graphs are graphs in which a vertical line extends from each data point down to the horizontal axis. Vertical line graph sometime also called as column graph. A line parallel to the y-axis is called a vertical line.

Equation of the vertical line: x = 0.

Graph for x = 5

### Horizontal Line Graph

Horizontal line graphs are graphs in which a horizontal line extends from each data point parallel to he earth. Horizontal line graph sometime also called as row graph. A line parallel to the x-axis is called a vertical line.

Equation of the horizontal line: y = 0.

Graph for y = 4

## Straight Line Graph

A line graph is a graph formed by segments of straight lines that join the plotted points that represent given data. The line graph is used to solve changing condition, often over a certain time interval. A general linear function has the form y = mx + c , where m and c are constants.

The fundamental rule at the rear of sketching a linear graph is that we require only two points to graph a straight line. The subsequent procedure is followed in drawing linear graphs:
• By substituting two dissimilar values for x in the equation y = mx + c, we get two values for y. Thus, we get two points (x1, y1) and (x2, y2) on the line.
• Plot the horizontal line and vertical line select the suitable scale for both the axis. If the given table values are large choose the scale for that particular value. It depends on given value.
• Plot the two points in the Cartesian plane of the paper.
• Join the two points using line segment and extend to two directions. The closed figure was obtained it is the required linear graph.

## Double Line Graph

A double line graph is a line graph with two lines. A graph that compares two different subjects over a period of time. A double line graph shows how things change over a period of time. Double line graph show two line graphs within one chart. Double line graphs are used to compare trends and patterns between two subjects.

### Make a Double Line Graph

Steps to Make a Double Line Graph:

Step 1: Use the data from the table to choose an appropriate scale.

Step 2: Draw and label the scale on the vertical and horizontal axis.

Step 3: List the each item and locate the points on the graph for both the lines.

Step 4: Connect the points with line segments separately of both the lines.

Step 5: Draw two line graphs within one chart.

### Double Line Graph Example

The points on the double line graph show the average monthly rainfall in the two cities (city 1, city 2). The separate lines that are made by connecting the points for each city.

## Inequality Line Graph

Graph of inequality helps represented inequalities of absolute value on number line. When solving and graphing absolute value inequalities, we need to evaluate the inequality twice for both the positive and negative possibilities for the variable.

### Solved Example

Question: Sketch the solution on number line |x + 2| $\leq$ 5.
Solution:

Given inequality |x + 2| $\leq$ 5

Step 1: Change the inequality into a compound inequality

- 5 $\leq$ x + 2 $\leq$ 5

Step 2:
Subtract 2 from all three sides to get

- 5 - 2 $\leq$ x + 2 - 2 $\leq$ 5 - 2

= - 7 $\leq$ x $\leq$ 3

Step 3: Place this value on a number line