Write an equation for a line perpendicular to y=-5x-2 and passing through the point (-10,-5)

To find an equation of a line perpendicular to \(y = -5x - 2\) and passing through the point \((-10, -5)\), we need to follow these steps:

1. **Find the slope of the given line**:
   The equation of the given line is \(y = -5x - 2\). The slope of this line is \(-5\).

2. **Determine the slope of the perpendicular line**:
   The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line is:
   \[
   m = -\frac{1}{-5} = \frac{1}{5}
   \]

3. **Use the point-slope form of the line equation**:
   The point-slope form of the equation of a line is given by:
   \[
   y - y_1 = m(x - x_1)
   \]
   Here, \(m = \frac{1}{5}\) and the point \((x_1, y_1) = (-10, -5)\).

4. **Substitute the slope and the point into the point-slope form**:
   \[
   y - (-5) = \frac{1}{5}(x - (-10))
   \]
   Simplify this equation:
   \[
   y + 5 = \frac{1}{5}(x + 10)
   \]

5. **Distribute and solve for \(y\)**:
   \[
   y + 5 = \frac{1}{5}x + 2
   \]
   \[
   y = \frac{1}{5}x + 2 - 5
   \]
   \[
   y = \frac{1}{5}x - 3
   \]

Therefore, the equation of the line perpendicular to \(y = -5x - 2\) and passing through the point \((-10, -5)\) is:
\[
y = \frac{1}{5}x - 3
\]

Would you like more details or have any questions?

Here are 5 questions you can ask next:
1. How do you find the equation of a line given two points?
2. What is the distance formula between two points in a plane?
3. How do you find the midpoint of a line segment?
4. What is the general form of the equation of a circle?
5. How do you convert a quadratic equation from standard form to vertex form?

**Tip:** When working with linear equations, always remember that perpendicular lines have slopes that are negative reciprocals of each other.

Learn how to find the equation of a line perpendicular to y=-5x-2 passing through the point (-10,-5). This problem covers key concepts in linear equations, including slope calculation, point-slope form, and perpendicular lines. Suitable for students in Grades 7-9.

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