The equation of the line provided is:

$y = 3x + 1$

This is in the slope-intercept form $y = mx + b$, where:

• $m$ is the slope of the line (in this case, $m = 3$),
• $b$ is the y-intercept (in this case, $b = 1$).

Steps to graph the line:

1. Plot the y-intercept: The y-intercept is where the line crosses the y-axis. This happens at the point $(0, 1)$, so the first point to plot is $(0, 1)$.

2. Use the slope to find another point: The slope $m = 3$ means "rise over run." This translates to:

   • "Rise" = 3 units up.
   • "Run" = 1 unit to the right.

   Starting from the point $(0, 1)$, move 3 units up and 1 unit to the right. This will take you to the point $(1, 4)$.

3. Plot the second point: After applying the slope, plot the point $(1, 4)$.

4. Draw the line: Connect the two points $(0, 1)$ and $(1, 4)$ to form the line.

Would you like to know more details on how to graph, or how the slope works in greater depth?

Relative Questions:

1. How do we determine the slope of a line from its equation?
2. What does the y-intercept represent in a linear equation?
3. How can you graph lines with negative slopes?
4. How would this graph change if the slope were 1/2 instead of 3?
5. What happens to the graph when the y-intercept is negative?

Tip:

To quickly sketch a line, always start with the y-intercept and use the slope to find another point on the line.