Which function rule represents the data in the table below? Show your work.
Input(x) 1 2 3 4 5
Output (y) 9 14 19 24 29
y = 4 + 5x
y = 3 + 6x
y = 5 + 4x
y = 6 + 3x
To find the function rule, we need to find the pattern among the inputs and outputs. From the table, we can see that the output increases by 5 for every increase of 1 in the input. This means that the slope of the line is 5. To find the y-intercept, we can look at where the line crosses the y-axis, which is when x is 0. From the options given, only y = 4 + 5x satisfies these conditions.
Substituting x = 1, 2, 3, 4, 5 into the function rule, we can check that the outputs match the ones in the table. For example, when x = 3, y = 4 + 5(3) = 19, which matches the output value in the table.
Therefore, the function rule that represents the data in the table is y = 4 + 5x.