To find the linear equation for the length of the corn bed (y) in terms of the number of rows (x), we can use the given information from Gina's previous two gardens.

Let's create two ordered pairs of the form (x, y) using the information provided:

Ordered pair 1: (2 rows, 5 feet)
Ordered pair 2: (5 rows, 11 feet)

Using these two ordered pairs, we can calculate the slope (m) of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values from the ordered pairs:

m = (11 - 5) / (5 - 2)
m = 6 / 3
m = 2

Now that we have the slope (m), we can find the y-intercept (b) using the equation:

y = mx + b

We can choose either of the two ordered pairs to substitute into the equation and solve for b. Let's use the first ordered pair (2 rows, 5 feet):

5 = 2(2) + b
5 = 4 + b
b = 5 - 4
b = 1

Therefore, the linear equation for the length of the corn bed (y) in terms of the number of rows (x) is:

y = 2x + 1