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A line is defined by the equation y = negative x + 3. Which shows the graph of this line?

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

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

On a coordinate plane, a line goes through points (0, 0) and (2, 6).

On a coordinate plane, a line goes through points (negative 2, 6) and (0, 0).

1 answer

The equation of the line is given as \( y = -x + 3 \). This is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

From the equation \( y = -x + 3 \):

  • The slope (\( m \)) is \(-1\).
  • The y-intercept (\( b \)) is \(3\), meaning the line crosses the y-axis at the point \((0, 3)\).

To find another point on the line, we can choose \( x = 3 \): \[ y = -3 + 3 = 0 \] So, when \( x = 3 \), \( y = 0\), which gives us the point \((3, 0)\).

Thus, the line passes through the points \((0, 3)\) and \((3, 0)\).

Now, we will examine the given options:

  1. On a coordinate plane, a line goes through points (0, 3) and (3, 0). ✔️ This matches the points we found on the line.
  2. On a coordinate plane, a line goes through points (0, negative 3) and (0, 3). ❌ The y-intercept is \(3\), not \(-3\).
  3. On a coordinate plane, a line goes through points (0, 0) and (2, 6). ❌ This line does not have the correct slope or intercept.
  4. On a coordinate plane, a line goes through points (negative 2, 6) and (0, 0). ❌ This line also does not match the equation given.

Therefore, the correct graph of the line defined by \( y = -x + 3 \) is the first option: On a coordinate plane, a line goes through points (0, 3) and (3, 0).