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Which of the following graphs is represented by the equation y=x−6
?(1 point)
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The equation \( y = x - 6 \) represents a linear graph. To identify the characteristics of this graph:

  1. Slope: The coefficient of \( x \) is 1, which indicates that the slope of the line is 1. This means that for every 1 unit increase in \( x \), \( y \) increases by 1 unit.

  2. Y-intercept: The equation can be rewritten in slope-intercept form \( y = mx + b \), where \( b \) is the y-intercept. Here, the y-intercept is -6, indicating that the line crosses the y-axis at the point (0, -6).

  3. X-intercept: To find the x-intercept (the point where the graph crosses the x-axis), set \( y = 0 \): \[ 0 = x - 6 \implies x = 6 \] So, the x-intercept is at the point (6, 0).

In summary, the graph of \( y = x - 6 \) is a straight line with a slope of 1, crossing the y-axis at (0, -6) and the x-axis at (6, 0). If you have the options for the graphs, the correct graph would be a line with these properties.