Question
describe the vertical translation between y =5x+2 and y=-7x 2 points below the equation y=-7x y=5x+2 -7 points below the equation y=-7x 2 pints above the equation y=-7x
which is the correct answer
which is the correct answer
Answers
GPT-4o mini
To find the vertical translation between the lines \( y = 5x + 2 \) and \( y = -7x \), we can analyze their y-intercepts and compare their vertical positions.
1. **Slope and Y-Intercept of Each Line**:
- The equation \( y = 5x + 2 \) has a slope of 5 and a y-intercept of 2 (meaning at \( x=0 \), \( y=2 \)).
- The equation \( y = -7x \) has a slope of -7 and a y-intercept of 0 (at \( x=0 \), \( y=0 \)).
2. **Vertical Position**:
- The line \( y = 5x + 2 \) is located at \( y=2 \) when \( x=0 \).
- The line \( y = -7x \) is at \( y=0 \) when \( x=0 \).
- Therefore, \( y = 5x + 2 \) is 2 units above \( y = -7x \) at \( x=0 \).
3. **Vertical Translation**:
- The vertical translation from \( y = -7x \) to \( y = 5x + 2 \) can be described as moving vertically upwards by 2 units.
Based on the description provided, the correct answer is the statement that says **"2 points above the equation \( y = -7x \)"**.
In summary, \( y = 5x + 2 \) is 2 units above \( y = -7x \).
1. **Slope and Y-Intercept of Each Line**:
- The equation \( y = 5x + 2 \) has a slope of 5 and a y-intercept of 2 (meaning at \( x=0 \), \( y=2 \)).
- The equation \( y = -7x \) has a slope of -7 and a y-intercept of 0 (at \( x=0 \), \( y=0 \)).
2. **Vertical Position**:
- The line \( y = 5x + 2 \) is located at \( y=2 \) when \( x=0 \).
- The line \( y = -7x \) is at \( y=0 \) when \( x=0 \).
- Therefore, \( y = 5x + 2 \) is 2 units above \( y = -7x \) at \( x=0 \).
3. **Vertical Translation**:
- The vertical translation from \( y = -7x \) to \( y = 5x + 2 \) can be described as moving vertically upwards by 2 units.
Based on the description provided, the correct answer is the statement that says **"2 points above the equation \( y = -7x \)"**.
In summary, \( y = 5x + 2 \) is 2 units above \( y = -7x \).