To graph the equation \(x - y = 6\) using the form \(y = mx + b\), we first convert the equation into slope-intercept form (which is \(y = mx + b\)).
Starting with the original equation: \[ x - y = 6 \]
We can isolate \(y\): \[ -y = -x + 6 \]
Multiplying through by -1 gives us: \[ y = x - 6 \]
Now, in this equation \(y = x - 6\), the slope \(m\) is \(1\) and the y-intercept \(b\) is \(-6\).
To graph this equation:
- Start at the y-intercept \((0, -6)\).
- From there, use the slope: for every 1 unit you move to the right (positive direction on the x-axis), you move up 1 unit (positive direction on the y-axis).
You can also find another point by plugging in another value for \(x\):
- If \(x = 3\): \[ y = 3 - 6 = -3 \] So another point is \((3, -3)\).
Plotting the points \((0, -6)\) and \((3, -3)\) and drawing a line through them gives the graph of the equation.
Given your descriptions, the correct image would be the one where a line drawn through points includes the coordinates (0, -6) as this corresponds correctly with our derived equation \(y = x - 6\).
The specific plotting of other points from your options does not seem to match the equation \(x - y = 6\) or \(y = x - 6\) correctly, so please refer to the graph that clearly shows that relationship. If you can provide those images or correct specific coordinates as needed, I can further assist!