Point a and b belong to the graph of the function y = kx + b. Determine the slope k, if A (6; 5) and B (12; 11)

1) Substitute the coordinates of point A into the equation y = kx + b.

A (6; 5), x = 6, y = 5.

5 = k * 6 + b;

6k + b = 5.

2) Substitute the coordinates of point B into the equation y = kx + b.

B (12; 11), x = 12, y = 11.

11 = k * 12 + b;

12k + b = 11.

3) We combine the equations into a system and, having solved it, we find the coefficient k.

{6k + b = 5; 12k + b = 11.

Let us express the variable b from the first equation of the system in terms of k.

b = 5 – 6k.

Let us substitute the expression (5 – 6k) in the second equation of the system instead of the variable b.

12k + (5 – 6k) = 11;

12k + 5 – 6k = 11;

6k + 5 = 11;

6k = 11 – 5;

6k = 6;

k = 6: 6;

k = 1.

Answer. k = 1.