Question

graph the line. y = x - 6

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=x - 6\), the slope \(m = 1\) and the y - intercept \(b=-6\).

Step2: Plot the y-intercept

The y - intercept is \(-6\), so we plot the point \((0,-6)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m = 1=\frac{1}{1}\), which means we move up 1 unit and to the right 1 unit from the point \((0,-6)\). So from \((0,-6)\), moving up 1 and right 1 gives us the point \((1,-5)\). We can also move down 1 and left 1 from \((0,-6)\) to get \((-1,-7)\) (optional, but helps in drawing the line).

Step4: Draw the line

Connect the points \((0,-6)\), \((1,-5)\) (and other points if needed) with a straight line. The line should have a slope of 1 and pass through the y - axis at \((0,-6)\).

Answer:

To graph \(y = x-6\):

1. Plot the y - intercept \((0,-6)\).
2. Use the slope \(m = 1\) to find another point (e.g., from \((0,-6)\), move 1 unit up and 1 unit right to get \((1,-5)\)).
3. Draw a straight line through the plotted points. The line will have a slope of 1 and cross the y - axis at \((0,-6)\).