Question

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Part 1
Graph the linear equation.
xminusyequals5

Answer 1

To graph the linear equation \( x - y = 5 \), we can first rearrange it into slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the equation:

\[
x - y = 5
\]

We can isolate \( y \):

1. Subtract \( x \) from both sides:
\[
-y = -x + 5
\]

2. Multiply through by -1 to solve for \( y \):
\[
y = x - 5
\]

Now, the equation is in slope-intercept form \( y = x - 5 \), which indicates that:
- The slope \( m \) is 1
- The y-intercept \( b \) is -5

### Plotting the Graph
1. **Y-Intercept**: Start at the y-intercept (0, -5) on the graph.
2. **Slope**: The slope of 1 means that for every increase of 1 unit in \( x \), \( y \) increases by 1 unit.

From the y-intercept (0, -5), if you move one unit to the right (to \( x = 1 \)), you move one unit up to \( y = -4 \). This gives you another point: (1, -4).

### Additional Points
You can also find more points by choosing other values for \( x \):
- If \( x = 2 \), then \( y = 2 - 5 = -3 \) (Point: (2, -3))
- If \( x = -1 \), then \( y = -1 - 5 = -6 \) (Point: (-1, -6))

### Drawing the Line
1. Plot the points you have found, such as (0, -5), (1, -4), and (2, -3).
2. Draw a straight line through these points, extending it in both directions.

This is how you graph the linear equation \( x - y = 5 \).

### Summary of Key Points:
- Points to plot: (0, -5), (1, -4), (2, -3), (-1, -6)
- The line has a slope of 1 and crosses the y-axis at -5.