Describe the level curves of the function.Sketch the level curves for the given c- values.

Question

Quizplus · Accepted Answer

The function has the form f(x,y) = ax + by. This is a linear function of x and y, which means the level curves are straight lines. Specifically, the level curves for values of c will be lines with slope -a/b.

For choice B, the value of c is 0, which means the level curves are lines with slope -1/2. These lines will be straight and have a negative slope, so B is the best choice.

For choices A and C, the value of c is nonzero, which means the level curves are not straight lines.

For choices D and E, the value of a is zero, which means the function is constant along lines parallel to the y-axis. Therefore, the level curves are vertical lines, not lines with slope -1/2.

Describe the Level Curves of the Function