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