Line Charts
Table of Content:
Line Charts - Aptitude Formulas
Definition
Line Chart: A line chart is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments.
Basic Components of a Line Chart
- Title: Describes what the line chart is about.
- Axis: The x-axis (horizontal) and y-axis (vertical) provide a reference for the data.
- Data Points: Represent individual data values plotted on the chart.
- Line Segments: Connect the data points to show trends over time.
- Labels: Describe the data categories and values.
Formulas Related to Line Charts
Slope of a Line
If two points on a line are \( (x_1, y_1) \) and \( (x_2, y_2) \), the slope \( m \) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]Equation of a Line
The equation of a line with slope \( m \) passing through the point \( (x_1, y_1) \) is:
\[ y - y_1 = m(x - x_1) \]Finding Total Value
If the values represented by the data points are \( y_1, y_2, y_3, \ldots, y_n \), the total value is:
\[ \text{Total Value} = y_1 + y_2 + y_3 + \cdots + y_n \]Finding Average Value
If the values represented by the data points are \( y_1, y_2, y_3, \ldots, y_n \), the average value is:
\[ \text{Average Value} = \frac{y_1 + y_2 + y_3 + \cdots + y_n}{n} \]Example Problems
Example 1: Finding Slope
If two points on a line are (2, 3) and (5, 7), the slope is:
\[ m = \frac{7 - 3}{5 - 2} = \frac{4}{3} \]Example 2: Equation of a Line
Using the slope \( m = \frac{4}{3} \) and the point (2, 3), the equation of the line is:
\[ y - 3 = \frac{4}{3}(x - 2) \quad \Rightarrow \quad y = \frac{4}{3}x - \frac{8}{3} + 3 \quad \Rightarrow \quad y = \frac{4}{3}x + \frac{1}{3} \]Example 3: Finding Total Value
If the values represented by the data points are 10, 20, 30, and 40, the total value is:
\[ \text{Total Value} = 10 + 20 + 30 + 40 = 100 \]Example 4: Finding Average Value
If the values represented by the data points are 10, 20, 30, and 40, the average value is:
\[ \text{Average Value} = \frac{10 + 20 + 30 + 40}{4} = \frac{100}{4} = 25 \]