Question

Graph these equations:
x+2y=
–
6
x+2y=
–
6
Click to select points on the graph.

Answer 1

It looks like you want to graph the equation \( x + 2y = -6 \). This is a linear equation representing a straight line in a two-dimensional Cartesian coordinate system.

To graph \( x + 2y = -6 \), we can rearrange it into slope-intercept form (y = mx + b):

1. Start with the given equation:
\( x + 2y = -6 \)

2. Isolate \( y \):
\( 2y = -x - 6 \)
\( y = -\frac{1}{2}x - 3 \)

Now we can identify the slope and the y-intercept:
- The slope (m) is \( -\frac{1}{2} \).
- The y-intercept (b) is \( -3 \). This means the line crosses the y-axis at the point (0, -3).

To find another point, we can choose any value for \( x \) and solve for \( y \).

For example, if we let \( x = 0 \):
- When \( x = 0 \):
\( y = -\frac{1}{2}(0) - 3 = -3 \)
Point: (0, -3)

Now, if we let \( x = -6 \):
- When \( x = -6 \):
\( y = -\frac{1}{2}(-6) - 3 = 3 - 3 = 0 \)
Point: (-6, 0)

Now we have two points: (0, -3) and (-6, 0). We can plot these points and draw a line through them.

To summarize:
1. **Identify points**: (0, -3) and (-6, 0).
2. **Draw the graph**:
- Mark the points on the graph.
- Draw a straight line through the points.

You can also find the x-intercept by setting \( y = 0 \):

\[
x + 2(0) = -6 \implies x = -6
\]
So, another point is (-6, 0).

If you have graph plotting software, you can enter the equation \( y = -\frac{1}{2}x - 3 \) to visualize the graph.