Question
Which graph displays the additive linear equation y=x−4
?(1 point)
Responses
1.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.
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, 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.
Image with alt text: 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.
4.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.
?(1 point)
Responses
1.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.
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, 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.
Image with alt text: 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.
4.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.
Answers
Answered by
GPT-4o mini
To determine which graph displays the additive linear equation \( y = x - 4 \), we can analyze the equation:
1. **Intercepts**:
- The **y-intercept** (where \( x = 0 \)):
\[
y = 0 - 4 = -4
\]
So the point \( (0, -4) \) is on the graph.
- The **x-intercept** (where \( y = 0 \)):
\[
0 = x - 4 \implies x = 4
\]
So the point \( (4, 0) \) is on the graph.
2. **Quadrants**: Given the intercepts \( (0, -4) \) and \( (4, 0) \), the line will pass through quadrants:
- Quadrant 4 (as it goes up from \((4, 0)\) to \((0, -4)\))
- Quadrant 1 (as it continues in the positive direction from \((0, -4)\))
Now, looking at the provided options for a line passing through the points \( (4, 0) \) and \( (0, -4) \):
- **Graph 1**: Passes through \( (4, 0) \) and \( (0, -4) \). This is the correct representation.
- **Graph 2**: Passes through points \( (0, 4) \) and \( (-4, 0) \). This is incorrect.
- **Graph 3**: Passes through points \( (0, 4) \) and \( (4, 0) \). This is also incorrect.
- **Graph 4**: Passes through points \( (0, -4) \) and \( (-4, 0) \). This is incorrect.
Therefore, the correct graph that displays the equation \( y = x - 4 \) is **Graph 1**.
1. **Intercepts**:
- The **y-intercept** (where \( x = 0 \)):
\[
y = 0 - 4 = -4
\]
So the point \( (0, -4) \) is on the graph.
- The **x-intercept** (where \( y = 0 \)):
\[
0 = x - 4 \implies x = 4
\]
So the point \( (4, 0) \) is on the graph.
2. **Quadrants**: Given the intercepts \( (0, -4) \) and \( (4, 0) \), the line will pass through quadrants:
- Quadrant 4 (as it goes up from \((4, 0)\) to \((0, -4)\))
- Quadrant 1 (as it continues in the positive direction from \((0, -4)\))
Now, looking at the provided options for a line passing through the points \( (4, 0) \) and \( (0, -4) \):
- **Graph 1**: Passes through \( (4, 0) \) and \( (0, -4) \). This is the correct representation.
- **Graph 2**: Passes through points \( (0, 4) \) and \( (-4, 0) \). This is incorrect.
- **Graph 3**: Passes through points \( (0, 4) \) and \( (4, 0) \). This is also incorrect.
- **Graph 4**: Passes through points \( (0, -4) \) and \( (-4, 0) \). This is incorrect.
Therefore, the correct graph that displays the equation \( y = x - 4 \) is **Graph 1**.