Question
Calculate the equation of a line that is perpendicular to the line shown on the graph and that also shares the same y-intercept.
Answers
GPT-4o mini
To find the equation of a line that is perpendicular to another line and shares the same y-intercept, you would follow these steps:
1. **Identify the original line's equation**: If the original line is given in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.
2. **Determine the slope of the perpendicular line**: If the slope of the original line is m, the slope of the line that is perpendicular to it will be -1/m. This is because the slopes of two perpendicular lines are negative reciprocals of each other.
3. **Use the same y-intercept**: The y-intercept remains the same as that of the original line.
4. **Write the equation**: Substitute the slope of the perpendicular line and the y-intercept into the slope-intercept form (y = mx + b).
### Example:
Let's say the original line's equation is \(y = 2x + 3\).
- The slope (m) is 2, and the y-intercept (b) is 3.
- The slope of the perpendicular line would be \(-1/2\).
- Since it shares the same y-intercept, we have \(b = 3\).
The equation of the perpendicular line would be:
\[
y = -\frac{1}{2}x + 3
\]
If you have specific values for the original line, please provide them and I can calculate the perpendicular line's equation directly!
1. **Identify the original line's equation**: If the original line is given in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.
2. **Determine the slope of the perpendicular line**: If the slope of the original line is m, the slope of the line that is perpendicular to it will be -1/m. This is because the slopes of two perpendicular lines are negative reciprocals of each other.
3. **Use the same y-intercept**: The y-intercept remains the same as that of the original line.
4. **Write the equation**: Substitute the slope of the perpendicular line and the y-intercept into the slope-intercept form (y = mx + b).
### Example:
Let's say the original line's equation is \(y = 2x + 3\).
- The slope (m) is 2, and the y-intercept (b) is 3.
- The slope of the perpendicular line would be \(-1/2\).
- Since it shares the same y-intercept, we have \(b = 3\).
The equation of the perpendicular line would be:
\[
y = -\frac{1}{2}x + 3
\]
If you have specific values for the original line, please provide them and I can calculate the perpendicular line's equation directly!