What linear function equation can be represented by the set of ordered pairs? (-4,-6) (0,-3) (4,0) (12,6)

Check out the slope of the line segment connecting (-4,-6) and (0,-3):
         -3 - (-6)        3
m = =
           0 - (-4)       4

Now use the point slope formula to derive the function:

y - 0 = (3/4)(x - 4)         or    y = (3/4)(x - 4 (answer)

check:  Does (12,6) satify this formula?  

Try again:  Find the line connecting (4,0) and (12,6):
         6 - 0        6        3
m = = =     This is good news, since we got m = 3/4 earlier.
        12-4         8        4

Try again to obtain the equation of this line with slope 3/4:

Use y = mx + b.  Using the point (0, -3),    -3 = (3/4)(0) + b.  Then b = -3
and the line is y = (3/4)x - 3.

Check this using the point (-4,-6):  Is the following true?  -6 = (3/4)(-4) - 3
                                                                                           -6 = -3 - 3   TRUE

The desired linear function is y = (3/4)x - 3.