Question

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

Answer 1

To graph the equations \( x - y = -6 \) and \( x + y = 2 \), we first need to rearrange each equation to the slope-intercept form \( y = mx + b \).

1. **For the first equation \( x - y = -6 \)**:
\[
-y = -x - 6 \implies y = x + 6
\]

2. **For the second equation \( x + y = 2 \)**:
\[
y = -x + 2
\]

Now we can plot these two lines:

### Plotting \( y = x + 6 \):
- This line has a slope of 1 and a y-intercept of 6. It passes through points like:
- (0, 6)
- (1, 7)
- (-6, 0)

### Plotting \( y = -x + 2 \):
- This line has a slope of -1 and a y-intercept of 2. It passes through points like:
- (0, 2)
- (2, 0)
- (-2, 4)

### Intersection Point
To find the intersection point of these two lines, set \( x + 6 = -x + 2 \):
\[
x + x = 2 - 6
\]
\[
2x = -4 \implies x = -2
\]
Substituting \( x = -2 \) in either equation:
\[
y = -(-2) + 2 = 2 + 2 = 4
\]
Thus, the intersection point is (-2, 4).

### Summary of Points to Plot:
- For \( y = x + 6 \): (0, 6), (1, 7), (-6, 0)
- For \( y = -x + 2 \): (0, 2), (2, 0), (-2, 4) (intersection point)

You can use graphing software or graph paper to plot these points and draw the lines. The lines will intersect at the point (-2, 4).