Answer:
-13
Explanation:
You want the missing value in the given table.
Relation
It is often useful to plot the values given on a graph to see what sort of curve those values define. Doing that here reveals that the points all lie on the same line.
Once you determine the relation is linear, you can set about finding exactly what it is. The points (0, 2) and (2, -4) are the easiest to use for this purpose.
Slope-intercept equation for a line
The point (0, 2) tells you the line has a y-intercept of 2. Its equation can be written in the form ...
y = mx + b . . . . . . . . where m is the slope, and b is the y-intercept (2)
The slope can be found from the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-4 -2)/(2 -0) = -6/2 = -3
Then the relation can be written ...
y = -3x +2
Missing value
Using x=5, we find the missing value to be ...
y = -3(5) +2 = -15 +2
y = -13
The missing value in the table is -13.
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Additional comment
Once you plot the points on a graph, you can draw a line through them and see where that line intersect x=5.
In the attached, we used the linear regression capability of a graphing calculator to find the equation of the line. (A spreadsheet can do the same thing for you.)