Question

Graph the line that passes through the given point and has the given slope m.
1.) (-2,6); m= -1/2

Answer 1

To graph the line that passes through the point (-2, 6) with a slope of m = -1/2, follow these steps:

1. **Identify the point:** You have the point (-2, 6), which is where the line will cross.

2. **Use the slope:** The slope of -1/2 means that for every 2 units you move to the right (in the positive x-direction), you move 1 unit down (in the negative y-direction).

3. **Plot the starting point:** Begin by plotting the point (-2, 6) on the graph.

4. **Use the slope to find another point:**
- Start at (-2, 6).
- Move 2 units to the right:
\[
-2 + 2 = 0 \quad \text{(new x-coordinate)}
\]
- Move 1 unit down:
\[
6 - 1 = 5 \quad \text{(new y-coordinate)}
\]
- This gives you the new point (0, 5).

5. **Plot the new point:** Mark the point (0, 5) on the graph.

6. **Draw the line:** Use a ruler to connect the points (-2, 6) and (0, 5) and extend the line in both directions.

7. **Label the line (optional):** You may label the line with its equation, which can be written in point-slope form or slope-intercept form.

The slope-intercept form \(y = mx + b\):
- Using the slope-intercept form, we can rearrange as follows:
\[
y - 6 = -\frac{1}{2}(x + 2)
\]
Simplify to find the equation:
\[
y = -\frac{1}{2}x + 5
\]

Thus, the equation of the line is \(y = -\frac{1}{2}x + 5\).

Now you've successfully graphed the line! If you have graphing paper or software, you can plot this accurately.