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.
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