To graph the line with a y-intercept of $-2$ and a slope of $\frac{3}{2}$, follow these steps:

1. Plot the y-intercept:

• The y-intercept is the point where the line crosses the y-axis. For this line, the y-intercept is $-2$, meaning the point $(0, -2)$.
• On the graph, place a point at $(0, -2)$, which is 2 units down on the y-axis.

2. Use the slope to find another point:

• The slope $\frac{3}{2}$ tells us how steep the line is. It means that for every 2 units you move to the right (along the x-axis), the line rises by 3 units (up the y-axis).
• Starting from $(0, -2)$, move 2 units to the right (to $(2, -2)$) and then move 3 units up (to $(2, 1)$).

3. Draw the line:

• Draw a straight line through the two points $(0, -2)$ and $(2, 1)$.
• This will be the graph of the line with the given slope and y-intercept.

Would you like further details on how to graph this or more information about slopes and intercepts?

Related Questions:

1. How do you determine the slope of a line from two points on a graph?
2. What is the equation of a line in slope-intercept form?
3. How does changing the slope affect the steepness of the line?
4. How can you graph a line if given two points instead of slope and intercept?
5. What happens to the graph of a line if the slope is negative?

Tip:

Always remember: the slope $\frac{\text{rise}}{\text{run}}$ tells you how much to move up or down (rise) and how much to move left or right (run) from one point to the next!