Write a linear function if the graph passes through the point (2;4) and (-4;-2).

We'll write the standard form of a linear function
f(x):

f(x) = ax + b

In this
case, the graph of the function is passing through the given
points.

By definition, a point belongs to a curve if the
coordinates of the point verify the equation of the
curve.

(2;4) is on the line y = ax+b if and only
if:

4 = a*(2) + b

2a + b = 4
(1)

(-4;-2) belongs to the graph of y = ax+b if and only
if:

-2 = -4a + b

-4a + b = -2
(2)

We'll subtract (2) from
(1)

2a + b + 4a - b = 4 +
2

We'll eliminate and combine like
terms:

6a = 6

a =
1

From (1)=>2 + b
= 4

b = 4 - 2

b =
2

The function f(x) whose graph is passing through the
given points is:

f(x) = x +
2