To determine which graph represents the equation \( y = x - 3 \), we can analyze the equation itself.
The equation \( y = x - 3 \) is in slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope (which is 1 in this case),
- \( b \) is the y-intercept (which is -3 in this case).
This means that the line crosses the y-axis at \( (0, -3) \).
Next, we can find another point on the line by substituting a value for \( x \). If \( x = 3 \): \[ y = 3 - 3 = 0 \] This means that the line also passes through the point \( (3, 0) \).
Now let's review the options given:
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First option: A line through points \( (-3, 0) \) and \( (0, -3) \).
- The y-intercept here is \( -3 \), but it does not go through \( (3, 0) \).
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Second option: A line through points \( (0, -1) \) and \( (1, 2) \).
- The y-intercept is \( -1 \) and the slope is 3, so this does not represent the equation.
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Third option: A line through points \( (0, -3) \) and \( (3, 0) \).
- This option has the correct y-intercept of \( -3 \) and passes through the point \( (3, 0) \).
Thus, the graph that represents the equation \( y = x - 3 \) is the third option, which goes through points \( (0, -3) \) and \( (3, 0) \).