Describe in words and sketch the level curves for the funciton and given \(c\) values. \(f(x,y)=3x-2y\) for \(c=-2,0,2\)

For \(c=0\), \(3x-2y=0\) or \(y=\frac{3}{2}x\)

For \(c=2\), \(3x-2y=2\) or \(y=\frac{3}{2}x-1\)

For \(c=-2\) \(3x-2y=-2\) or \(y=\frac{3}{2}x+1\)

Generically for \(c\) the level curves can be summarized as \(y=\frac{3}{2}x-\frac{c}{2}\) and are clearly lines.

funct.1 <- function(x) {3/2*x}
funct.2 <- function(x) {3/2*x-1}
funct.3 <- function(x) {3/2*x+1}

ggplot(data=data.frame(x=0), mapping=aes(x=x)) +
  stat_function(fun=funct.1, color='blue') +
  stat_function(fun=funct.2, color='blue') +
  stat_function(fun=funct.3, color='blue') +
  xlim(-3, 3) +
  ylim(-3, 3)