Question

Which is true for all pairs of values in this table? X1,2,3,4 y 0,-2,-4,-6

Answer 1

Given data:

X               Y
1                 0
2              - 2
3              - 4 
4              - 6

From the above table,
We have to see what sort of function is it showing.
Therefore,
Taking the first difference of the y-values.
We get,
-2 , -2 , -2

The first difference is constant for all the y-values, that is -2. Therefore it is a linear function,
So,
using the general form,
                                         y = mx + b
where m represent the slope and b represents the y-intercept.

Now,
We will use two coordinate points to find out the slope,

Let them be: (1,0) and (2,-2)
So,
m = 2 / -1
m = -2

Now the y-intercept,

As we know that,
                             y = -2x + b

Take any point from the table, let it be (1,0)

substituting it into the equation, we get;
                                                                    0 = -2(1) + b
                                                                    b = 2

Hence our equation is:
                                       y = - 2x + 2