Line y = kx + b passes through points A (-1; -9) and B (2; 6) Write the equation of this straight line.

In order to find the coefficients k and b of the straight line y = kx + b, if it passes through points A (-1; -9) and B (2; 6).

Let’s compose and solve the system of equations:

-9 = -k + b;

6 = 2k + 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 = k – 9;

6 = 2k + k – 9.

We solve the second equation of the system:

6 = 2k + k – 9;

6 + 9 = 3k;

3k = 15;

k = 15: 3;

k = 5.

System of equations:

b = k – 9 = 5 – 9 = -4;

k = 5.

We write down the equations of the straight line:

y = 5x – 4.

Answer: y = 5x – 4 equation of a straight line.