What is the rule for the function shown in the table?
A table is shown with the first row titled x and the second row titled y.
The first row contains the numbers negative 1, 0, 1, and 2.
The second row contains the numbers negative 2, 1, 4, and 7.
A. y equals one-third x plus 1
B. y = 3x + 1
C. y equals one-third x
D. y equals one-half x plus 1
To find the rule for the function shown in the table, we need to observe the pattern of how the x-values are related to the y-values.
If we examine the differences between consecutive x and y values, we see that the differences are not consistent. However, if we look at the differences between consecutive y-values, we see that they are always increasing by 3. From this, we can deduce that the function is linear with a slope of 3.
To find the y-intercept, we can substitute any of the given points into the equation y = 3x + b and solve for b. For example, if we use the point (0,1), we get:
1 = 3(0) + b
b = 1
Therefore, the rule for the function shown in the table is B. y = 3x + 1.