Line y = kx + b passes through points A (-2: 11) and B (12: 4). Write the equation for this straight line.

In order to find the coefficients k and b of the straight line y = kx + b, if it passes through the points A (-2; 11) and B (12; 4).

Let’s compose and solve the system of equations:

11 = -2k + b;

4 = 12k + b;

We solve the system using the substitution method. Let us express the variable b from the first equation of the system in terms of k.

System:

b = 11 + 2k;

4 = 12k + 11 + 2k.

We solve the second equation of the system:

4 = 12k + 11 + 2k;

14k = 4-11;

14k = -7;

k = -7: 14;

k = -0.5.

System of equations:

b = 11 + 2k = 11 – 1 = 10;

k = -0.5.

Let us write down the equations of the straight line:

y = -0.5x + 10.

Answer: y = -0.5x + 10 equation of a straight line.