Question

Graph these equations:
2x–y=2
x+y=4
Click to select points on the graph.

Answer 1

To graph the equations \( 2x - y = 2 \) and \( x + y = 4 \), we'll first rewrite them in slope-intercept form (y = mx + b) to identify their slopes and y-intercepts.

1. For the equation \( 2x - y = 2 \):
\[
-y = -2x + 2
\]
\[
y = 2x - 2
\]
- The slope (m) is 2, and the y-intercept (b) is -2.

2. For the equation \( x + y = 4 \):
\[
y = -x + 4
\]
- The slope (m) is -1, and the y-intercept (b) is 4.

### Steps to Graph:

1. **Graph \( y = 2x - 2 \)**:
- Start at the y-intercept (0, -2).
- Use the slope (rise/run = 2/1) to find another point: (1, 0).

2. **Graph \( y = -x + 4 \)**:
- Start at the y-intercept (0, 4).
- Use the slope (rise/run = -1/1) to find another point: (1, 3).

### Points for the Graph:
- From the first equation, you can plot the points (0, -2) and (1, 0).
- From the second equation, you can plot the points (0, 4) and (1, 3).

### Intersection Point:
To find the intersection of these two lines, set them equal to each other:

\[
2x - 2 = -x + 4
\]
Combine and solve for x:
\[
2x + x = 4 + 2
\]
\[
3x = 6 \quad \rightarrow \quad x = 2
\]

Substitute \( x = 2 \) back into one of the original equations:
\[
y = 2(2) - 2 = 2
\]
So, the intersection point is (2, 2).

### Graph Summary:
- The first line crosses the y-axis at (0, -2) and (1, 0).
- The second line crosses the y-axis at (0, 4) and (1, 3).
- The lines intersect at (2, 2).

You can now click to select and plot these points on the graph.