Which equation represents a line which is perpendicular to the line y=-1/2x - 6?

To find the equation of a line that is perpendicular to the line \( y = -\frac{1}{2}x - 6 \), we need to determine the slope of the perpendicular line.

### Steps:
1. **Identify the slope of the given line**:
   - The given equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.
   - The slope of the given line is \( m = -\frac{1}{2} \).

2. **Determine the slope of the perpendicular line**:
   - The slope of a line perpendicular to another is the negative reciprocal of the original slope.
   - The negative reciprocal of \( -\frac{1}{2} \) is \( \frac{2}{1} = 2 \).

3. **Write the equation of the perpendicular line**:
   - The general form of the equation of a line with slope \( m = 2 \) is \( y = 2x + c \), where \( c \) is the y-intercept.

Therefore, the equation of a line that is perpendicular to the line \( y = -\frac{1}{2}x - 6 \) will be of the form:

\[ y = 2x + c \]

Where \( c \) is a constant that could be any real number, depending on where the line crosses the y-axis.

Would you like to solve for a specific perpendicular line through a given point, or do you have any other questions?

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**Related Questions**:
1. How do you find the y-intercept of a line?
2. What is the significance of the slope in a linear equation?
3. How do you determine if two lines are parallel?
4. What is the general form of a linear equation?
5. How do you convert a linear equation from standard form to slope-intercept form?
6. What are the properties of perpendicular lines in a coordinate plane?
7. How do you find the equation of a line given two points?
8. What is the difference between the slope of a line and the y-intercept?

**Tip**: Remember that the slope of a perpendicular line is always the negative reciprocal of the original slope.

Learn how to find the equation of a line that is perpendicular to y = -1/2x - 6. Understand the concept of perpendicular lines and how to apply the perpendicular lines theorem in geometry. Suitable for Grades 7-9.

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