What is value of a + b calculus

I need some help with steps, there's a table but I can't copy and paste so I will list values, I apologize for this.
x = 5, f(x) = a
x = 10, f(x) = 32
x = 15 , f(x) = b
If f is a linear function, what is value of a + b?

64.

Since f(x) is a linear function, it has the form f(x) = mx + c.

f(5) = 5m + c = a
f(10) = 10m + c = 32
f(15) = 15m + c = b

a + b =
(5m + c) + (15m + c) =
20m + 2c =
2(10m + c) =
2(32) =
64.

If it is a linear function, then the slope or rate of change has to be identical.

You are given a point (10, 32) and two others with variables (5, a) and (15, b)
Use your formula for slope (y1 - y2)/(x1 - x2) where (x1, y1) and (x2, y2) are given points on the line

(32 - a) / (10 - 5) = (32 - a) / 5

(b - 32) / (15 - 10) = (b - 32) / 5

(b - a) / (15 - 5) = (b - a) / 10

All these values are equal

(32 - a)/ 5 = (b - a) / 10 Multiply both side by 10
2(32 - a) = b - a
64 - 2a = b - a
64 = b + a