Certainly! Here are the steps to graphing a linear equation in the form \( y = mx + b \):
Step 1: Identify the slope (m) and y-intercept (b).
- The slope (m) indicates the steepness of the line and the direction (positive or negative).
- The y-intercept (b) is the point where the line crosses the y-axis.
Step 2: Plot the y-intercept.
- Start by plotting the point (0, b) on the graph, where b is the y-intercept.
Step 3: Apply the slope.
- The slope is represented as a fraction \( \frac{rise}{run} \). The rise is the vertical change (how much to move up or down) and the run is the horizontal change (how much to move right or left).
- From the y-intercept point, use the rise and run to find another point on the line. For example, if the slope is \( \frac{2}{3} \), you would go up 2 units (rise) and then to the right 3 units (run) and plot that point.
Step 4: Draw the line.
- Use a ruler to draw a straight line through the points you've plotted, extending it in both directions.
This method provides a clear and systematic way to graph any linear equation in the slope-intercept form \( y = mx + b \).