Question

Graph these equations:
x–y=2
3x–2y=6
Click to select points on the graph.

Answer 1

To graph the equations \( x - y = 2 \) and \( 3x - 2y = 6 \), we can first rewrite them in slope-intercept form ( \( y = mx + b \) ) to make plotting easier.

1. **For the equation \( x - y = 2 \):**

Rearranging gives:
\[
y = x - 2
\]

This means the slope \( m = 1 \) and the y-intercept \( b = -2 \).

2. **For the equation \( 3x - 2y = 6 \):**

Rearranging gives:
\[
-2y = -3x + 6 \quad \Rightarrow \quad y = \frac{3}{2}x - 3
\]

Here, the slope \( m = \frac{3}{2} \) and the y-intercept \( b = -3 \).

Now, let's find points for both lines to graph:

### Points for \( y = x - 2 \):
- If \( x = 0 \): \( y = 0 - 2 = -2 \) (point (0, -2))
- If \( x = 2 \): \( y = 2 - 2 = 0 \) (point (2, 0))
- If \( x = 4 \): \( y = 4 - 2 = 2 \) (point (4, 2))

### Points for \( y = \frac{3}{2}x - 3 \):
- If \( x = 0 \): \( y = \frac{3}{2}(0) - 3 = -3 \) (point (0, -3))
- If \( x = 2 \): \( y = \frac{3}{2}(2) - 3 = 0 \) (point (2, 0))
- If \( x = 4 \): \( y = \frac{3}{2}(4) - 3 = 3 \) (point (4, 3))

### Graphing:
- Plot the points for \( y = x - 2 \): (0, -2), (2, 0), (4, 2)
- Plot the points for \( y = \frac{3}{2}x - 3 \): (0, -3), (2, 0), (4, 3)

### Intersection Point:
Notice both lines intersect at (2, 0).

Now you can create a visual graph by plotting these points and drawing lines through them. The first line will slope upwards at a 45-degree angle, and the second line will be steeper, starting lower and moving higher.

Let me know if you'd like any more help!