Generating correlated vectors (X,Y) , whereby rho = f(x) 'hockey stick'

Question

I want to simulate depended (with changing correlation rho) variables to 'reproduce' this figure.

Correlation Breakpoint
rho = 0 for X=x <= 2.4
rho = 0.5 for X=x > 2.4

Bivariate Distribution Y|X
X = N ~ (mu_x, sd_x)
Y|X = N ~ (mu_x + sd_x/sd_y*rho(Y-mu_y), (1-rho^2)sd_x)

Given are:
mu_x = 3.13; sd_x = 0.6
mean_y = 31.3; sd_y = 6.7

My code works for generating correlated data, but misses the "breakpoint". Here's my code for the plot above:

X = rnorm(n, mean_x, sd_x)
Y = rnorm(n, mean_y + sd_y/sd_x * rho*(X-mean_x), (1-rho^2)*sd_y)

How do I make rho = f(x)? At the moment I glue the two distributions together to get a hockey stick like scatter block.:

 # Correlated Vectors (X, Y) - Hockey Stick 
 set.seed = 47
 n = 729
 mean_x = 3.13; sd_x = 0.6  # FEV
 mean_y =  31.3; sd_y = 6.7 # O2max

 # rho and breakpoint
 rho = 0.7; breakpoint = 3.5
 index_break = sum(X<breakpoint)

 # Generate X distributuion
 X = rnorm(n, mean_x, sd_x)

 # Generate Y disrtribution parts
 Y_rho = vector(); Y = vector()
 Y_rho = rnorm(n, mean_y + sd_y/sd_x*rho*(X-mean_x), (1-rho^2)*sd_y[1:index_break]
 Y = rnorm(n, mean_y, sd_y)[(index_break+1):length(FEV)]
 Y = c(Y_rho, Y)

 # plot
 plot(X, Y)

Thanks much in advance.