Final answer:
When capital and labor are perfect substitutes in a production function, the isoquants are straight lines because the substitution rate between capital and labor is constant.
Step-by-step explanation:
a straight line:
If capital and labor are perfect substitutes in a production function, the isoquants for this function will be a straight line. This is because perfect substitutes mean that the producer can replace capital with labor, or vice versa, without affecting the output. With perfect substitutability, the rate at which capital can be substituted for labor (and vice versa) is constant, therefore the isoquants, which show all the combinations of labor and capital that can produce a given level of output, will be linear.
It's important to distinguish this from the situation where capital is fixed. Such scenarios highlight how the output depends on the variable factor, usually labor. But when considering the long-term production function, where all factors are variable, and assuming perfect substitutability between labor and capital, the mentioned straight-line isoquants are characteristic.