x y
2 2
4 8
7 17
10 26
x y
2 2
4 8
7 17
10 26
First, since you are given several points for this table, you need to find the slope of the function using any two points given in the table.
Recall the formula for the slope of a function given any two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is as follows:
Slope = (y_{2} - y_{1})/(x_{2} - x_{1})
Let's use the first point and the last point in the table to solve for the slope:
Point 1: (x_{1}, y_{1}) = (2, 2) and Point 2: (x_{2}, y_{2}) = (10, 26)
Slope = (26 - 2)/(10 - 2) = 24/8 = 3 ==> Slope = 3
Using the slope formula and the value for the slope we've found, we can find the y value of a point when its x value is 12 by designating this as the second point and choosing any other point in the table as the first point:
Point 1: (x_{1}, y_{1}) = (2, 2) , Point 2: (x_{2}, y_{2}) = (12, y) , and Slope = 3
3 = (y - 2)/(12 - 2)
3 = (y - 2)/10
After we cross multiply, we arrive at the following:
y - 2 = 30
Add 2 to both sides of the equation to solve for y:
y = 32
Thus, when x equals 12 y equals 32 (i.e., x=12, y=32).