Question
Describe the vertical translation between
y = 5x + 2 and y = - 7x. (1 point)
2 points below the equation
У =-7х
2 points above the equation
У =-7x
-7 points below the equation
У =- 7х
• y=5x + 2
y = 5x + 2 and y = - 7x. (1 point)
2 points below the equation
У =-7х
2 points above the equation
У =-7x
-7 points below the equation
У =- 7х
• y=5x + 2
Answers
GPT-4o mini
To describe the vertical translation between the two equations \( y = 5x + 2 \) and \( y = -7x \), we need to analyze how the position of one graph is affected relative to the other.
1. **Identify the Reference Point**: Let's first identify the base equation, which in this case will be \( y = -7x \).
2. **Vertical Translation**: The equation \( y = 5x + 2 \) can be transformed in relation to \( y = -7x \) to look for a vertical shift.
- The change in the y-intercept can give us insight into the vertical translation. For \( y = -7x \), there is no y-intercept (meaning it crosses through the origin) and for \( y = 5x + 2 \), the y-intercept is at \( (0, 2) \).
3. **Calculate the Vertical Shift**:
- At \( x = 0 \):
- For \( y = -7x \): \( y = -7(0) = 0 \)
- For \( y = 5x + 2 \): \( y = 5(0) + 2 = 2 \)
- The vertical distance between these points is \( 2 - 0 = 2 \).
4. **Direction of Translation**: Since \( y = 5x + 2 \) is 2 units **above** the graph of \( y = -7x \) at the point where \( x = 0 \), we can conclude that the line \( y = 5x + 2 \) is translated **upward** by 2 units from the line \( y = -7x \).
In conclusion, **the vertical translation between \( y = 5x + 2 \) and \( y = -7x \) is 2 points above the equation \( y = -7x \)**.
1. **Identify the Reference Point**: Let's first identify the base equation, which in this case will be \( y = -7x \).
2. **Vertical Translation**: The equation \( y = 5x + 2 \) can be transformed in relation to \( y = -7x \) to look for a vertical shift.
- The change in the y-intercept can give us insight into the vertical translation. For \( y = -7x \), there is no y-intercept (meaning it crosses through the origin) and for \( y = 5x + 2 \), the y-intercept is at \( (0, 2) \).
3. **Calculate the Vertical Shift**:
- At \( x = 0 \):
- For \( y = -7x \): \( y = -7(0) = 0 \)
- For \( y = 5x + 2 \): \( y = 5(0) + 2 = 2 \)
- The vertical distance between these points is \( 2 - 0 = 2 \).
4. **Direction of Translation**: Since \( y = 5x + 2 \) is 2 units **above** the graph of \( y = -7x \) at the point where \( x = 0 \), we can conclude that the line \( y = 5x + 2 \) is translated **upward** by 2 units from the line \( y = -7x \).
In conclusion, **the vertical translation between \( y = 5x + 2 \) and \( y = -7x \) is 2 points above the equation \( y = -7x \)**.