Define a linear function by the formula, the graph of which passes through the points A (1.13) and B (-2.10).

We know that the linear function y = kx + b passes through the points with coordinates A (1; 13) and B (-2; 10). In order to write the formula of the function, we must find the values of the coefficients k and b.

To do this, we will compose and solve the system of equations:

13 = k + b;

10 = -2k + b.

We solve by substitution method. Express the variable b from the first expression and substitute it into the second.

b = 13 – k;

10 = -2k + 13 – k.

We solve the equation:

-2k – k = -13 + 10;

-3k = -3;

k = -3: (-3);

k = 1.

System:

b = 13 – 1 = 12;

k = 1.

Let’s make the equation:

y = x + 12.