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
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