Ginas previous garden she was able to plant 2 rows of corn in a 5 foot long space and 5 rows of corn in a 11 foot long space. find a linear equation for the length of the bed (y) in which she can fit x rows of corn.
To find a linear equation for the length of the bed (y) in which Gina can fit x rows of corn, we need to determine the relationship between the number of rows of corn and the length of the bed.
From the given information, we have two data points:
- In a 5-foot long space, Gina can plant 2 rows of corn.
- In an 11-foot long space, Gina can plant 5 rows of corn.
Let's assign the number of rows of corn as x and the length of the bed as y. To find the linear equation, we need to find the slope (m) and the y-intercept (b).
First, let's find the slope (m):
Slope (m) = (change in y) / (change in x)
(change in y) = (5 rows - 2 rows) = 3 rows
(change in x) = (11 feet - 5 feet) = 6 feet
Slope (m) = (3 rows) / (6 feet) = 1/2
So, the slope (m) is 1/2.
Now, let's find the y-intercept (b):
For one of the data points, we can choose the 5-foot long space where Gina can plant 2 rows of corn.
Therefore, x = 2 and y = 5.
Using the slope-intercept form of a linear equation (y = mx + b), we can substitute the values into the equation and solved for b:
5 = (1/2)(2) + b
5 = 1 + b
b = 5 - 1
b = 4
So, the y-intercept (b) is 4.
Now we have the slope (m) and the y-intercept (b), we can write the linear equation as:
y = (1/2)x + 4
Therefore, the linear equation for the length of the bed (y) in which Gina can fit x rows of corn is y = (1/2)x + 4.