Which graph displays the additive linear equation y=x−4

Question

?(1 point)
Responses

1. A coordinate plane shows a straight line passing through quadrants 2, 3, and 4. Both the x and y axes range from negative 10 to 10. A solid line with a bi-directional arrow passes through points at left parenthesis 0 comma negative 4 right parenthesis and left parenthesis negative 4 comma 0 right parenthesis.
Image with alt text: A coordinate plane shows a straight line passing through quadrants 2, 3, and 4. Both the x and y axes range from negative 10 to 10. A solid line with a bi-directional arrow passes through points at left parenthesis 0 comma negative 4 right parenthesis and left parenthesis negative 4 comma 0 right parenthesis.

2. A coordinate plane shows a straight line passing through quadrants 1, 2, and 3. Both the x and y axes range from negative 10 to 10. A solid line with a bi-directional arrow passes through points at left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 4 comma 0 right parenthesis.
Image with alt text: A coordinate plane shows a straight line passing through quadrants 1, 2, and 3. Both the x and y axes range from negative 10 to 10. A solid line with a bi-directional arrow passes through points at left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 4 comma 0 right parenthesis.

3. A coordinate plane shows a straight line passing through quadrants 1, 3, and 4. Both the x and y axes range from negative 10 to 10. A solid line with a bi-directional arrow passes through points at left parenthesis 4 comma 0 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis.
Image with alt text: A coordinate plane shows a straight line passing through quadrants 1, 3, and 4. Both the x and y axes range from negative 10 to 10. A solid line with a bi-directional arrow passes through points at left parenthesis 4 comma 0 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis.

4. A coordinate plane shows a straight line passing through quadrants 1, 2, and 4. Both the x and y axes range from negative 10 to 10. A solid line with a bi-directional arrow passes through points at left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.

Answer 1

To determine which graph displays the linear equation \(y = x - 4\), we can analyze the equation.

1. Identifying Key Points:

   • The y-intercept occurs where \(x = 0\): \[ y = 0 - 4 = -4 \] So, one point is \((0, -4)\).

   • The x-intercept occurs where \(y = 0\): \[ 0 = x - 4 \implies x = 4 \] So, another point is \((4, 0)\).

2. Analyzing the Quadrants:

   • The point \((0, -4)\) is located on the negative side of the y-axis (Quadrants 3 and 4).
   • The point \((4, 0)\) is located on the positive side of the x-axis (Quadrant 1).

3. Conclusion:

   • The line will pass through Quadrants 1 (from the x-intercept at (4,0)) and 4 (from the y-intercept at (0,-4)).
   • Therefore, it would be a straight line that goes from Quadrant 1 to Quadrant 4.

Now let's review the provided options:

• Option 3 states a line passing through points \((4, 0)\) and \((0, -4)\) and through quadrants 1, 3, and 4. This option matches our analysis since the line does indeed cross into Quadrant 3.

Thus, the graph that displays the additive linear equation \( y = x - 4 \) is Option 3.