Graph x-y=6 using the form y=mx+b

Answer 1

To graph the equation \( x - y = 6 \) using the slope-intercept form \( y = mx + b \), you will need to first convert the given equation into that form.

Starting with the equation:
\[ x - y = 6 \]

1. Solve for \( y \):
\[ -y = -x + 6 \]
\[ y = x - 6 \]

Now, the equation is in the slope-intercept form \( y = mx + b \), where:
- \( m \) (the slope) is 1
- \( b \) (the y-intercept) is -6

To graph this equation, follow these steps:

1. **Plot the y-intercept**:
- The y-intercept (\( b \)) is -6. This is the point where the line crosses the y-axis.
- Plot the point (0, -6) on the graph.

2. **Use the slope to find another point**:
- The slope (\( m \)) is 1, which can be written as \( \frac{1}{1} \). This means that for every 1 unit you move to the right on the x-axis, you move 1 unit up on the y-axis.
- Starting from the y-intercept (0, -6), move 1 unit to the right to (1, -6) and then 1 unit up to (1, -5). Plot the point (1, -5).

3. **Draw the line**:
- Using a ruler, draw a straight line through the points (0, -6) and (1, -5). Extend the line in both directions.
- Make sure to label the line with the equation \( y = x - 6 \).

This is how you graph the line \( x - y = 6 \) using the slope-intercept form.