To graph a line with a y-intercept of -3 and a slope of 3, we can use the slope-intercept form of a linear equation:

$y = mx + b$ where:

• $m$ is the slope, and
• $b$ is the y-intercept.

Given:

• Slope $m = 3$,
• Y-intercept $b = -3$.

Steps to graph the line:

1. Start at the y-intercept: Plot the point $(0, -3)$ on the y-axis.
2. Use the slope to find another point: The slope is 3, which means for every 1 unit increase in $x$, $y$ increases by 3 units. From the point $(0, -3)$, move 1 unit to the right (positive $x$) and 3 units up (positive $y$) to plot the next point, $(1, 0)$.
3. Draw the line: Connect these two points with a straight line, and extend it across the grid.

If you'd like, I can guide you through using any tools to visualize it more clearly.

Do you need further details or a different explanation?

Relative questions:

1. How do you find the equation of a line given two points?
2. What happens to the line if the slope is negative?
3. How would the graph change if the y-intercept was positive?
4. How can you graph a line if given the slope and a point other than the y-intercept?
5. Can the slope of a vertical line be determined? Why or why not?

Tip:

When working with slopes, remember that the slope represents the "rise over run," i.e., how much the line goes up (or down) for a given horizontal movement.