Create a plot, flipping axes while keeping the same scale - r

Question

I'm plotting some graphs to introduce the concept of mathematical function to highschool students. Right now, I'd like to give them an example of what is NOT a function, by plotting an horizontal parabola:
x <- seq(from = -3, to = 3, by = 0.001)
y <- -x^2 + 5
grafico <- ggplot()+
geom_hline(yintercept = 0)+
geom_vline(xintercept = 0)+
geom_line(mapping = aes(x = x, y = y),color="darkred",size=1)+
theme_light()+
xlab("")+
ylab("")+
scale_x_continuous(breaks = seq(from = -100, to = 100, by = 1))+
scale_y_continuous(breaks = seq(from = -100, to = 100, by = 1))+
coord_flip(ylim = c(-1.5,5.5), xlim = c(-3,3),expand = FALSE)
print(grafico)
Which outputs the following image:
This is quite close to what I want, but I would like both axes' scales to match, to keep things simple for the students. For this, I'd tried using coord_equal, but unluckily, it seems to cancel coord_flip's effects:
x <- seq(from = -3, to = 3, by = 0.001)
y <- -x^2 + 5
grafico <- ggplot()+
geom_hline(yintercept = 0)+
geom_vline(xintercept = 0)+
geom_line(mapping = aes(x = x, y = y),color="darkred",size=1)+
theme_light()+
xlab("")+
ylab("")+
scale_x_continuous(breaks = seq(from = -100, to = 100, by = 1))+
scale_y_continuous(breaks = seq(from = -100, to = 100, by = 1))+
coord_flip(ylim = c(-1.5,5.5), xlim = c(-3,3),expand = FALSE)+
coord_equal()
print(grafico)
My question is: Is there a simple way to include coord_flip functionality into coord_equal?
For example, I know I can get coord_cartesian functionality by using the parameters ylim and xlim.

Answer 1

Based on your use case, it doesn't look like you really need to flip the coordinates: you can just reverse the order of inputs for x & y, and use geom_path() instead of geom_line() to force the plot to follow the order in your inputs.
The ggplot help file states:
geom_path() connects the observations in the order in which they
appear in the data. geom_line() connects them in order of the
variable on the x axis.
ggplot() +
geom_hline(yintercept = 0) +
geom_vline(xintercept = 0) +
geom_path(mapping = aes(x = y, y = x), color="darkred", size = 1) + # switch x & y here
theme_light() +
xlab("") +
ylab("") +
scale_x_continuous(breaks = seq(from = -100, to = 100, by = 1)) +
scale_y_continuous(breaks = seq(from = -100, to = 100, by = 1)) +
coord_equal(xlim = c(-1.5, 5.5), ylim = c(-3, 3), expand = FALSE) # switch x & y here