Lets assume that the input values are x values and the output values are y values.
Then you will have pairs of coordinate values as shown;
(-1,7) , (0,2) , (1,-3) , (2,-8), (3,-13), (4,-18)
Using the coordinates find the slope a;
(-1,7) and (0,2) ---------slope is change in y-values/ change in x-values , (2-7) /(0--1)
= -5/ 1 = -5
Do the same for the next pair of coordinates ,(0,2) and (1,-3) , (-3-2) / (1-0) = -5/1 = -5
If you continue the procedure to the next pair which is (1,-3) and (2,-8) to get the slope as : (-8- -3) / (2-1) = -5/1 = -5
This means that the slope is -5
The relation will be represented by the equation y= mx + c where m is the slope and c is the y-intercept
First plot the points to visualize the graph
From the plot, you notice that when the points are joined, a straight graph is formed sloping to the negative side and intersecting the y-axis at point (0,2).
So to determine the rule, we apply the equation y= mx + c with m= -5 and c =2
This gives y= -5 x + 2
The rule is f(x) = -5x +2 -----------answer