Provide the linear function if the representing graph passes through the points (2;3) and (-2;-3)?

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

f(x) = ax + b

We know,
from enunciation, that 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;3) is located on the graph of  y = ax+b if and
only if:

3 = a*(2) + b

2a + b
= 3 (1)

(-2;-3) belongs to the graph of y = ax+b if and
only if:

-3 = -2a + b

-2a + b
= -3 (2)

We'll add (2) to
(1)

2a + b -2a + b = 3-3

We'll
eliminate and combine like terms:

2b =
0

b = 0

From
(1)=>2a+b=3 => 2a = 3

a =
3/2

The linear function f(x), whose graph is
passing through the given points is: f(x) = 3x/2.