W6 - Finding Equation from Graphs

Linear Relations - Finding the Equation of a Line

1. General Concepts

• Finding the Equation of a Line: Involves determining the linear equation from a graph or set of points. Common formats of line equations include slope-intercept form (y = mx + b).

• Key Elements:

  • Slope (m): Represents the steepness of the line.

  • Y-intercept (b): The point where the line crosses the Y axis (at x=0).

2. Steps to Write the Equation from a Graph

• Identify two points on the line, preferably the intercepts (x-intercept and y-intercept).

• Calculate the slope (m) using the formula:( m = \frac{y_2 - y_1}{x_2 - x_1} )

• Plug the slope and y-intercept into the slope-intercept form:( y = mx + b )

3. Working with Table, Graph, and Verbal Representation

• Complete Missing Sections: For each question, provide the verbal description, table data, and corresponding graph.

Example Calculations

• Example 1:

  • Verbal: The line has a y-intercept at (0, 5) and a slope of 2.

  • Table:

    X	Y
    0	5

  • Graph: Plotting points from table and using slope to plot additional points.

  • Equation: ( y = 2x + 5 )

4. Sample Problems

• Problem 7:

  • Verbal: Line characteristics specified in detail.

  • Equation Calculation: Given (4, 0) and (0, -2) as intercepts, find slope and use values to derive equation.

• Problem 9:

  • Verbal: The line passes through points (2, 1) and (-3, 2).

  • Equation Calculation: Use point slope form ( y - y_1 = m(x - x_1) ) to derive the equation.

5. Example Equations

• Example 8:

  • Y-Intercept: 6, Slope: -1,

  • Equation: ( y = -1x + 6 )

• Example with Slope and Intercepts: To derive the slope and y-intercept from graphical representation:

  • X-Intercept: (4, 0)

  • Y-Intercept: (0, -2)

  • Equation: ( y = -2x + 8 )

6. Conclusion

• Understanding how to derive equations from graphs, tables, and verbal representation is crucial in linear relations. Practice by completing each representation and confirming through equation formulation.