Write down the equation of a straight line which has a normal vector n (5, -1) and passes through the point K (10,9).

From the condition, we know the normal vector with coordinates n (5; -1) and we also know that the straight line passes through the point K with coordinates (10; 9).

In order to write down the equation of the straight line, we will apply the following actions.

Let us recall the general form of the equation of the straight line: Ax + By + C = 0.

Coefficients A and B are the coordinates of the normal vector.

That is, A = 5, B = -1, then the equation will take the form:

5x – y + C = 0.

To find C, we substitute the coordinates of the point K into the equation instead of x and y:

5 * 10 – 9 + C = 0;

C = -41.

Equation of a straight line: 5x – y – 41 = 0.