Plotting different regression models on the same scatter plot

with the above data in df I did

library(tidyverse)

wdf <- filter(df,
              Fabric=='Walking')
wlm <- lm(formula = carcommute ~ poly(commutetime, 2,raw=TRUE),
          data = wdf)
wdf$pred <- predict(wlm,newdata = wdf)

adf <- filter(df,
              Fabric=='Automobile')
alm <- lm(formula = carcommute ~ poly(commutetime, 2,raw=TRUE),
          data = adf)
adf$pred <- predict(alm,newdata = adf)

tdf <- filter(df,
              Fabric=='Transit')
tlm <- lm(formula = carcommute ~ commutetime,
          data = tdf)
tdf$pred <- predict(tlm,newdata = tdf)

all_df <- wdf %>% union_all(adf) %>% union_all(tdf)

label_centers <- select(all_df,
                        carcommute,commutetime,
                        Fabric) %>% group_by(Fabric) %>% summarise_all(mean)

(equations_df <-tibble(
  Fabric = c("Walking","Automobile","Transit"),
  intercept = c(wlm$coefficients[[1]],
                alm$coefficients[[1]],
                tlm$coefficients[[1]]),
  deg1 = c(wlm$coefficients[[2]],
           alm$coefficients[[2]],
           tlm$coefficients[[2]]),
  deg2 = c(wlm$coefficients[[3]],
           alm$coefficients[[3]],
           NA_real_)) %>% mutate_if(is.numeric,~round(.,digits=3)))

equations_df$deg1sign <- if_else(equations_df$deg1>0,"+","-")
equations_df$deg2sign <- if_else(equations_df$deg2>0,"+","-")
equations_df$deg1 <- abs(equations_df$deg1)
equations_df$deg2 <- abs(equations_df$deg2)
equations_df$deg2sign <- if_else(is.na(equations_df$deg2sign),"",as.character(equations_df$deg2sign))
equations_df$deg2 <- if_else(is.na(equations_df$deg2),"",as.character(equations_df$deg2))
equations_df <- equations_df %>%
  mutate(eq_text = paste("y =",intercept,
                          deg1sign,deg1,"x",deg2sign,deg2,"x^2",sep = " "))

equations_df<- left_join(equations_df,label_centers)


all_df %>%
  ggplot(aes(x = commutetime, y = carcommute, color=Fabric, shape = Fabric)) +
  geom_point() +
  theme_minimal()+
  geom_point(size = 3.5, aes(color = Fabric, shape = Fabric))+
  geom_line(mapping = aes(y=pred), size = 1)+
  scale_color_manual(values = c("#00AFBB", "#E7B800", "#FC4E07"))+
  scale_fill_manual(values = c("#00AFBB", "#E7B800", "#FC4E07")) +
  geom_label(data=equations_df,mapping =aes(label=eq_text), alpha=.9,nudge_x = -8,nudge_y=4,show.legend = FALSE)