Having the function f(x)=ax+b which passes through the points A(-3,2) B(-4,5) and c=b-a, then which is the value of C ?

When a line having function

f(x) = ax + b   ... (1)

passes through two points A(x1, y1) and B(x2, y2), the value of a is given by:

a = (y2 - y1)/(x2 - x1)   ... (2)

As per the question the values of the coordinates of the points A and B are:

x1 = -3 and y1 = 2

x2 = -4 and y2 = 5

Substituting these values in equation (2) we get:

a = (5 - 2)/[-4 - (-1)}] = 3/-1 = -3

substituting this value of a and of x1, and y1 in equation (1) we get:

2 = -3*(-3) + b

Therefor: 2 = 9 + b

Or:

b = -7

It is given:

c = b - a

Substituting values of a and b in above equation we get:

c = -7 - (-3) = -4

Answer: c = -4