Question: Functions of several variables also have slopes. One way to see this is to reduce them to a function of a single variable by choosing

Functions of several variables also have slopes. One way to see this is to reduce them to a function of a single variable by choosing a constant value for other variables in the equation.

For example, consider the equation Y 5 10 1 3X 1 5Z.

a. If we assume a value for X of, say, 2, what is the relationship between Y and Z? What is its slope?

b. If we assume a value for Z of, say, 7, what is the relationship between Y and X? What is its slope?

c. How would your answers to parts a and b change if we had used different values for X and Z? Explain why the constant terms would change, but the slopes would not.

d. How might you change this basic equation in the body of this equation so that the slopes would depend on the specific values of X and Z chosen?

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