If the point (1,-2) is on the line x-2y+k=0 then find the value of k

To find the value of \( k \), we can substitute the coordinates of the given point \((1, -2)\) into the equation of the line \( x - 2y + k = 0 \).

Given:
- \( x = 1 \)
- \( y = -2 \)

Substitute these values into the equation:

\[
1 - 2(-2) + k = 0
\]

Simplify the equation:

\[
1 + 4 + k = 0
\]

\[
5 + k = 0
\]

Solve for \( k \):

\[
k = -5
\]

So, the value of \( k \) is \( \boxed{-5} \).

Would you like to go over any details or have any questions? Here are some related questions:

1. What is the general method for finding the equation of a line given a point and a slope?
2. How can you determine if a point lies on a given line without calculating \( k \)?
3. What does the value of \( k \) represent in the context of the line equation?
4. How would the equation of the line change if the point given was \((2, 3)\)?
5. Can you find the slope of the line from the equation \( x - 2y + k = 0 \)?

**Tip:** When dealing with line equations, always remember that substituting a point directly into the equation helps verify if it lies on the line.

If the point (1,-2) is on the line x-2y+k=0 then find the value of k.

Solve the problem of finding the value of k in the line equation x - 2y + k = 0, given that the point (1, -2) lies on the line. This solution involves substitution in the equation of a line, suitable for students in Grades 6-8.

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