To graph the equation $y = -0.5x - 2$, follow these steps:

1. Identify the slope and y-intercept:

• Slope (m): The coefficient of $x$, which is $-0.5$. This means for every 1 unit you move to the right on the x-axis, the value of y decreases by 0.5 units (the line slopes downward).
• Y-intercept (b): The constant term, which is $-2$. This is where the line crosses the y-axis.

2. Plot the y-intercept:

Start by plotting the point $(0, -2)$ on the graph.

3. Use the slope to find more points:

From $(0, -2)$, use the slope $-0.5$ to find additional points:

• Move 1 unit to the right (increase x by 1), then move 0.5 units down (decrease y by 0.5). This gives the point $(1, -2.5)$.
• Move another 1 unit to the right (increase x by 1), then move 0.5 units down. This gives the point $(2, -3)$.

4. Draw the line:

Connect the points with a straight line, extending it in both directions.

Would you like a visual of the graph, or do you have any questions?

5 Relative Questions:

1. How does the slope influence the steepness of the graph?
2. What happens to the graph if we change the slope to $-1$?
3. How do we graph a line if the slope is positive instead of negative?
4. How do we find the x-intercept of the equation $y = -0.5x - 2$?
5. What is the significance of the y-intercept in different contexts?

Tip:

When the slope is negative, the line always decreases from left to right.