The equation you provided, \( y = x - 9 \), represents a linear function. Here are some key characteristics of this equation:
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Slope: The coefficient of \( x \) is 1, which means the slope of the line is 1. This means that for every unit increase in \( x \), \( y \) increases by 1.
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Y-Intercept: The equation can be rewritten in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In this case, the y-intercept is -9, meaning the line crosses the y-axis at the point (0, -9).
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X-Intercept: To find the x-intercept, set \( y = 0 \): \[ 0 = x - 9 \ x = 9 \] Therefore, the x-intercept is at the point (9, 0).
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Graph: If you were to graph this equation, you would start at the point (0, -9) on the y-axis, and from there, you would rise 1 unit and run 1 unit to the right to plot another point. You could continue this pattern to draw the line.
If you have any specific questions about this equation or if you would like to explore certain aspects further, feel free to ask!