you buy only apples and bananas. Your budget is such that you can purchase 3 apples and 4 bananas or 9 apples and 2 bananas. Write down the equation for the budget line with bananas on the y-axis. Is that equation unique
Of course this is not unique. One could buy all apples, or all bananas. Notice that each banana is worth three apples, so one could buy 5 bananas, or 15 apples.
To write down the equation for the budget line with bananas on the y-axis, we can use the slope-intercept form of a linear equation: y = mx + b, where y is the dependent variable (banana quantity), x is the independent variable (apple quantity), m is the slope, and b is the y-intercept.
Given that you can purchase 3 apples and 4 bananas or 9 apples and 2 bananas, we can find the slope of the budget line using the formula: (change in y) / (change in x).
Slope = (change in banana quantity) / (change in apple quantity)
= (2 - 4) / (9 - 3)
= -2 / 6
= -1/3
Since the slope is negative, it implies that as the quantity of apples purchased increases, the quantity of bananas will decrease.
To find the y-intercept, we can substitute one of the given points into the equation and solve for b. Let's use the point (3, 4) where 3 apples and 4 bananas can be purchased.
4 = (-1/3)*3 + b
4 = -1 + b
b = 4 + 1
b = 5
Hence, the equation for the budget line with bananas on the y-axis is:
Banana Quantity (y) = (-1/3)*Apple Quantity (x) + 5
Regarding uniqueness, the equation for the budget line is determined by the given information and can be considered unique in this context.