Line Charts

• 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.

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 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:

\[ \text{Average Value} = \frac{10 + 20 + 30 + 40}{4} = \frac{100}{4} = 25 \]