To plot the line defined by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, follow these steps:

1. Identify the Slope and Y-Intercept:

   • The slope $m$ tells you how steep the line is. It indicates the rise (change in $y$) over the run (change in $x$).
   • The y-intercept $b$ is where the line crosses the y-axis. This is the point $(0, b)$.

2. Plot the Y-Intercept:

   • Start by plotting the point $(0, b)$ on the y-axis. This is where the line intersects the y-axis.

3. Use the Slope to Find Another Point:

   • From the y-intercept, use the slope $m$. If $m = \frac{\text{rise}}{\text{run}}$, move up (or down if $m$ is negative) by the rise and right by the run. For example, if $m = \frac{2}{3}$, go up 2 units and right 3 units from the y-intercept to plot another point.

4. Draw the Line:

   • Once you have at least two points, draw a straight line through them. This line represents all solutions to $y = mx + b$.

5. Extend the Line and Add Arrows (Optional):

   • Extend the line in both directions to cover the range of $x$ values you're interested in. Adding arrows on both ends indicates that the line continues infinitely.

Would you like a plot for a specific slope and y-intercept value, or do you have any questions?

Here are five follow-up questions to consider:

1. What does changing the slope $m$ do to the line?
2. How does changing the y-intercept $b$ affect the line’s position?
3. How would you plot a line if only two points on the line are given?
4. How can you determine if two lines are parallel from their equations?
5. How would you plot a vertical or horizontal line?

Tip: Always check your points after plotting to ensure they satisfy the equation $y = mx + b$.