Transform y so that y==x

Question

This is probably very trivial and I can't get my head around this.

Note: all the codes below are in R

I have the following x and y values:

y_values <- c(68.5626444935181, 74.9499148487446, 
79.8497409367012, 73.0839198881826, 69.3704162253844, 71.2955559142127, 
73.3039295493942, 80.4815231294542, 77.3386138482087, 76.7735812401891, 
83.1127314163547, 76.0379064535433, 76.3375388691764, 79.3073079200627, 
79.4969630108931, 75.4074011408933, 73.1746588455723, 74.7381647481472, 
76.0068878713895, 66.6933533294857, 77.2538702691301, 72.3045360297129, 
80.9516081348814, 81.5990676377598, 73.3101299846443, 74.542113081284, 
78.0547705030883, 70.7484704958974, 74.0914515886154, 70.0722061819694, 
77.1576715278398, 76.340436178083, 72.345917299701, 73.8302355573314, 
74.5860765982042, 72.0199091680495, 71.6603668197653, 76.2407368365496, 
73.085653645391, 71.6614849907091, 77.5958284776863, 69.2870233168088, 
91.4953861502152, 78.1859047973624, 72.2066485610847, 75.7656423615475, 
71.2736144202631, 73.8804703782756, 73.806815498892, 72.3512968378224
)

x_values <- c(66.714969241285, 74.6001367053999, 82.488038277512, 
79.9945317840055, 65.6650717703349, 74.930963773069, 82.2255639097745, 
84.7272727272727, 80.1667805878332, 81.1237183868763, 83.1414900888585, 
76.6124401913876, 82.2802460697198, 84.6507177033493, 85.0061517429939, 
84.4538619275461, 82.6110731373889, 79.6144907723855, 80.2816131237184, 
66.9665071770335, 79.1032125768968, 73.8427887901572, 80.6643882433356, 
79.4231032125769, 79.2809295967191, 89.4545454545455, 81.0635680109364, 
77.0307587149692, 77.4545454545455, 75.8441558441558, 77.7908407382092, 
78.4333561175666, 76.9405331510595, 76.9596719070403, 76.3991797676008, 
75.3246753246753, 73.6623376623377, 76.7081339712919, 74.9801777170198, 
71.2071086807929, 81.1811346548189, 65.3807245386193, 85.4654818865345, 
80.0328092959672, 65.161995898838, 81.9302802460697, 73.5037593984962, 
77.367053998633, 75.5652768284347, 72.6015037593985)

d <- data.frame(y_values=y_values, x_values=x_values)

If I plot y vs x this is what I have:

library(ggpmisc)
ggplot(d, aes(y = y_values, x = x_values)) +
  geom_smooth(method = "lm", se = FALSE, color = "lightgrey",  formula = y ~ x) +     geom_point( alpha=0.3) +
  stat_poly_eq(aes(label = paste0("atop(", ..eq.label.., ",", ..rr.label.., ")")), 
               formula = y ~ x, 
               parse = TRUE) 

y ~ x

I used the stat_poly_eq function from ggpmisc to get the line's equation

Now I want to transform y so that y == x and all the points are moved on the diagonal. I tried to extract the coefficients from the equation and transform y values like so:

transform_y <- function(raw_y, a=0.548,b=32.5){
  return(a*(raw_y-b))
}
d <- d %>% 
  mutate(y_values_new = transform_y(y_values) )

The new plot looks like this:

ggplot(d, aes(y = y_values_new, x = x_values)) +
  geom_smooth(method = "lm", se = FALSE, color = "lightgrey",  formula = y ~ x) +     geom_point( alpha=0.3) +
  stat_poly_eq(aes(label = paste0("atop(", ..eq.label.., ",", ..rr.label.., ")")), 
               formula = y ~ x, 
               parse = TRUE) 

y_new ~ x

All the points are aligned but not on the y=x diagonal.

What am I doing wrong here ?