Graph these equations:

Question

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.