How do I make a regression line for all values of my variable?

My plot:

plot(airbnb$distance_center,airbnb$price,pch=13,xlab="distance_center",ylab="price",bty="n")
mod <- lm(price~number_people+distance_center)

Now I want to include regression lines that show the correlation of price & distance_center - including all 6 characteristics of my variable "number_people"

My idea:

abline(mod$coeff[1],mod$coeff[2],lwd=2)
abline(mod$coeff[2],mod$coeff[2],lwd=2)
abline(mod$coeff[3],mod$coeff[2],lwd=2)

Unfortunately, I don't think this is quite right, I am not sure how to make a right step. Any idea?

You didn't post your data, so it's difficult to tell exactly how it's structured (is "number_people" numeric or factor?). In either case, you will need one regression line for each unique number_people.

Here I have created a similar data set with the same names as yours:

mod <- lm(price ~ number_people + distance_center, data = airbnb)

plot(airbnb$distance_center, airbnb$price,
     pch = 13, xlab = "distance_center", ylab = "price", bty = "n")

invisible(sapply(unique(airbnb$number_people), function(x) {
  abline(a = coef(mod)[1] + x * coef(mod)[2], b = coef(mod)[3])
}))

Made up data

set.seed(1)

airbnb <- data.frame(
  distance_center = sqrt(runif(100, 0, 10)^2 + runif(100, 0, 10)^2),
  number_people = sample(6, 100, TRUE))
  
airbnb$price <- 50 + airbnb$number_people * 
                50 / airbnb$distance_center + rnorm(100, 0, 5)^2

^{Created on 2022-05-28 by the reprex package (v2.0.1)}