Overview
This lesson explains how to draw a straight line by using the table method and intercept method, including step-by-step examples for both.
Table Method
- Create a table with columns for x and y values.
- Select at least two or three x-values (e.g., negative, zero, positive).
- Substitute each x-value into the line equation to find the corresponding y-value.
- Plot the (x, y) points on a graph, with x on the horizontal axis and y on the vertical axis.
- Draw a straight line through the plotted points.
Intercept Method
- The intercept method finds where the line crosses the x-axis and y-axis (the intercepts).
- To find the x-intercept, set y = 0 in the equation and solve for x.
- To find the y-intercept, set x = 0 in the equation and solve for y.
- Plot both intercept points on the graph.
- Draw a straight line through these two points.
Example: Drawing y = 3x - 6
- Table method: Choose x = -2 and x = 2, calculate y for both.
- For x = -2: y = 3(-2) - 6 = -12.
- For x = 2: y = 3(2) - 6 = 0.
- Plot points (-2, -12) and (2, 0).
- Intercept method:
- x-intercept: Set y = 0, solve 0 = 3x - 6 ⟹ x = 2.
- y-intercept: Set x = 0, solve y = 3(0) - 6 ⟹ y = -6.
- Plot points (2, 0) and (0, -6).
- Drawing either method gives the same straight line.
Key Terms & Definitions
- Table Method — A technique for plotting a line by calculating points from chosen x-values.
- Intercept Method — A technique using the x- and y-intercepts to graph a line.
- x-intercept — The point where a line crosses the x-axis (y = 0).
- y-intercept — The point where a line crosses the y-axis (x = 0).
Action Items / Next Steps
- Practice drawing lines using both the table method and intercept method for different linear equations.