To graph the equation \( x - y = 6 \) in the form \( y = mx + b \):
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Start by rearranging the equation to solve for \( y \): \[ x - y = 6 \quad \Rightarrow \quad -y = -x + 6 \quad \Rightarrow \quad y = x - 6 \]
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Now, we have the equation in slope-intercept form \( y = mx + b \), where:
- \( m = 1 \) (the slope)
- \( b = -6 \) (the y-intercept)
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To graph the line, start at the y-intercept (0, -6), and from there, use the slope:
- The slope \( m = 1 \) means for every 1 unit you move to the right on the x-axis, you also move up 1 unit on the y-axis.
- From (0, -6), moving to the right 1 unit to (1, -5) is one point on the line. Moving another unit to (2, -4) provides another point.
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You can also move in the opposite direction, starting from the y-intercept at (0, -6), moving left 1 unit down to (-1, -7).
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After plotting the points (0, -6), (1, -5), (2, -4), and (-1, -7), draw a straight line through these points.
The correct plotting should resemble a line that crosses the y-axis at (0, -6) and is seen rising towards the right as it moves in the direction where both x and y increase.
Given the two responses in your question, neither appears to correctly represent the line for the equation \( x - y = 6 \) or \( y = x - 6 \).
Make sure when graphing this equation, your line passes through the point (0, -6) and maintains a slope of 1.