Answer:
see attached
Explanation:
You want the empty cells of the given table filled in.
Slope
The differences between the first In values are ...
15 -7 = 8
21 -15 = 6
The corresponding differences between the Out values are ...
32 -16 = 16
44 -32 = 12
The ratios of Out differences to In differences are ...
16/8 = 2
12/6 = 2
These are constant, so we can conclude the relation is linear with a slope of m = 2.
Intercept
We can find the y-intercept by ...
b = y -mx
b = 16 -2(7) = 2 . . . . . . using (x, y) = (7, 16) and m=2
Relation
Then the equation of the output (y) in relation to the input (x) is ...
y = mx +b
y = 2x +2 . . . . . . . . . . . . . . table entry on 4th line from the bottom
Solving for x, we get ...
y -2 = 2x
(y -2)/2 = x
This tells us the input needed to give an output of y is (y -2)/2, the entry in the table on the 3rd line from the bottom.
Empty cells
We can use the equation for y when In is given:
- 2(25) +2 = 52
- 2(x) +2 = 2x +2
- 2(2x) +2 = 4x +2
- 2(x +3) +2 = 2x +6 +2 = 2x +8
And we can use the equation for x when Out is given:
- (22 -2)/2 = 20/2 = 10 . . . input value for output = 22
- (y -2)/2 . . . . . . . . . . . . . . input value for output = y
The completed table is attached.
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