Which graph represents the equation y = x – 3?

On a coordinate plane, a line goes through points (negative 3, 0) and (0, negative 3).
On a coordinate plane, a line goes through points (0, negative 1) and (1, 2).
On a coordinate plane, a line goes through points (0, negative 3) and (3, 0).

1 answer

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:

  1. First option: A line through points \( (-3, 0) \) and \( (0, -3) \).

    • The y-intercept here is \( -3 \), but it does not go through \( (3, 0) \).
  2. 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.
  3. 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 \( (3, 0) \).