Question

Graph the equation x−y=6 using the form y=mx+b.

Answer 1

To graph the equation \( x - y = 6 \) in the form \( y = mx + b \), we need to solve for \( y \).

Starting with the original equation:

\[
x - y = 6
\]

We can isolate \( y \) by moving \( x \) to the other side of the equation:

\[
-y = 6 - x
\]

Now, multiply by -1 to solve for \( y \):

\[
y = -x + 6
\]

This is now in the slope-intercept form \( y = mx + b \), where \( m = -1 \) (the slope) and \( b = 6 \) (the y-intercept).

### To Graph:

1. **Identify the y-intercept:** The y-intercept \( b \) is 6, which means the graph crosses the y-axis at the point (0, 6).

2. **Use the slope:** The slope \( m \) is -1, meaning for every 1 unit you move to the right (increase in \( x \)), you move down 1 unit (decrease in \( y \)). From the y-intercept (0, 6):
- Move 1 unit to the right to (1, 6) and then 1 unit down to (1, 5).
- Plot the second point (1, 5).

3. **Draw the line:** Connect these points with a straight line, and extend it in both directions.

### Points to plot:
- (0, 6) is the y-intercept.
- (1, 5) using the slope.

### Summary:
The line represented by the equation \( x - y = 6 \) in slope-intercept form is \( y = -x + 6 \). It has a slope of -1 and a y-intercept of 6.