Lines in the plane in practice

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Let (kinmathbb R). What is the slope of the line ((k-2)x+(6-k)y=3)? For which (k) is the slope of the line less than or equal to 0?

Exercise 2.

For which value of (kinmathbb R) are the lines [3x+ky=7,quad (2-k)x-5y=2] parallel?