Question

An equation is shown below.

x−y=2

Graph this equation by plotting two points on the coordinate plane.

Answer 1

To graph the equation \( x - y = 2 \), we can first rewrite it in slope-intercept form (y = mx + b) to make it easier to identify points.

Starting with the equation:

\[
x - y = 2
\]

We can rearrange it to solve for \( y \):

\[
-y = -x + 2 \implies y = x - 2
\]

Now, it's easy to see that the slope \( m = 1 \) and the y-intercept \( b = -2 \).

To graph this line, we'll plot two points. We can do this by selecting two values for \( x \) and then finding the corresponding values of \( y \).

### Point 1:
Let \( x = 0 \):

\[
y = 0 - 2 = -2
\]
So one point is \( (0, -2) \).

### Point 2:
Let \( x = 4 \):

\[
y = 4 - 2 = 2
\]
So another point is \( (4, 2) \).

### Summary of Points to Plot:
1. \( (0, -2) \)
2. \( (4, 2) \)

### Plotting the Points:
1. Plot the point \( (0, -2) \) on the coordinate plane.
2. Plot the point \( (4, 2) \) on the coordinate plane.

### Draw the Line:
Draw a straight line through the points \( (0, -2) \) and \( (4, 2) \) to represent the equation \( x - y = 2 \).

This line will extend infinitely in both directions, representing all the solutions to the equation \( x - y = 2 \).