Write down the equation of a linear function, the graph of which passes through the points M (2; 2) and N (1; -1).

Let’s write the equation of the linear function:

y = k * x + b;

To find out the coefficients k and b, we substitute the coordinates of points M and N into this equation. We get a system of equations:

2 = k * 2 + b;

-1 = k * 1 + b.

From the first equation, we express the coefficient b:

b = 2 – 2 * k; and substitute it into the second equation:

-1 = k + 2 – 2 * k;

-1 = -k + 2;

k = 3.

Substitute k = 3 in either of the two equations:

2 = 3 * 2 + b;

b = -4.

Hence, the equation of a linear function, the graph of which passes through the points M (2; 2) and N (1; -1) y = 3 * x – 4.