The graph of the function passes through the point (2, 1), and y increases by 4
when x increases by 1.

The graph in the attached figure

Step-by-step explanation:

In this problem I will assume the the function is linear

we have the point (2,1)

we know that

y increases by 4  when x increases by 1

Remember that the formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

so

The slope of the linear function is

Find the equation of the line in point slope form

substitute

Convert to slope intercept form

Isolate the variable y

see the attached figure to better understand the problem

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4