Asked by me
Graph these equations:
x+y=2
y=–x–6
x+y=2
y=–x–6
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
### 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.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.