line l has equation y=-4. find the distance between l and point f(-7,6)

The line \( l \) has the equation \( y = -4 \), which represents a horizontal line where the \( y \)-value is always \(-4\), regardless of the \( x \)-value.

The distance between a point and a horizontal line is simply the vertical distance between the point's \( y \)-coordinate and the line's \( y \)-coordinate. 

Given the point \( F(-7, 6) \), the \( y \)-coordinate of the point is 6, and the \( y \)-coordinate of the line is \(-4\). The vertical distance between them is:

\[
\text{Distance} = |6 - (-4)| = |6 + 4| = 10
\]

Thus, the distance between the line \( l \) and the point \( F(-7, 6) \) is **10 units**.

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Here are 5 related questions to explore:
1. What is the general formula for finding the distance between a point and a line in any orientation?
2. How can you find the distance between two points on a coordinate plane?
3. How do you calculate the distance between a point and a vertical line?
4. What is the shortest distance between a point and a line in 3D space?
5. How do you find the equation of a line that is parallel to a given line?

**Tip:** For any horizontal line, the distance between the line and a point is just the absolute difference in their \( y \)-coordinates.

Discover how to find the distance between a horizontal line, represented by y = -4, and the point F(-7, 6). This solution involves using the absolute difference between the y-coordinates of the line and the point, making it an essential concept for students learning coordinate geometry. Suitable for Grades 8-10.

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