Question

Graph these equations:
x+y=2
y=–x–6

Answer 1

To graph the equations \( x + y = 2 \) and \( y = -x - 6 \), we can start by rewriting them in slope-intercept form (if they're not already) and then plotting their points.

### 1. Graph \( x + y = 2 \)
To rearrange \( x + y = 2 \) into slope-intercept form \( y = mx + b \):

\[
y = -x + 2
\]

**Key points:**
- **Intercept:** When \( x = 0 \), \( y = 2 \) (point \( (0, 2) \))
- **Another point:** When \( y = 0 \), \( x = 2 \) (point \( (2, 0) \))

### 2. Graph \( y = -x - 6 \)
This equation is already in slope-intercept form:

\[
y = -x - 6
\]

**Key points:**
- **Intercept:** When \( x = 0 \), \( y = -6 \) (point \( (0, -6) \))
- **Another point:** When \( y = 0 \), \( -x - 6 = 0 \) so \( x = -6 \) (point \( (-6, 0) \))

### 3. Plotting the Points
You can plot the points on a coordinate plane:

1. For \( x + y = 2 \):
- Plot the points \( (0, 2) \) and \( (2, 0) \) and draw a line through them.

2. For \( y = -x - 6 \):
- Plot the points \( (0, -6) \) and \( (-6, 0) \) and draw a line through them.

### 4. Intersection Point (if needed)
To find the intersection of the two lines, set them equal to each other:

\[
-x + 2 = -x - 6
\]
This simplifies to \( 2 = -6 \), which is a contradiction, meaning the lines are parallel and do not intersect.

### Final Graph
- Draw both lines based on the points plotted.
- Label each line with its corresponding equation.

You’ll see that the first line (\( x + y = 2 \)) has a positive slope, while the second line (\( y = -x - 6 \)) has a negative slope, confirming they are parallel and will never cross.