Points 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)

The formula for the equation of a straight line passing through two given points has the form:

(x – x1) / (x2 – x1) = (y – y1) / (y2 – y1),

where (x1; y1) and (x2; y2) = coordinates of points.

Our points have coordinates (6; 5) and (12; 11). Means,

(x – 6) / (12 – 6) = (y – 5) / (11 – 5)

(x – 6) / 6 = (y – 5) / 6

x – 6 = y – 5

Let us bring the formula to the form y = kx + b

y = x – 1

We got that the slope is k = 1.

Answer: 1