[r] How to succinctly write a formula with many variables from a data frame?

I build this solution, reformulate does not take care if variable names have white spaces.

add_backticks = function(x) {
    paste0("`", x, "`")
}

x_lm_formula = function(x) {
    paste(add_backticks(x), collapse = " + ")
}

build_lm_formula = function(x, y){
    if (length(y)>1){
        stop("y needs to be just one variable")
    }
    as.formula(        
        paste0("`",y,"`", " ~ ", x_lm_formula(x))
    )
}

# Example
df <- data.frame(
    y = c(1,4,6), 
    x1 = c(4,-1,3), 
    x2 = c(3,9,8), 
    x3 = c(4,-4,-2)
    )

# Model Specification
columns = colnames(df)
y_cols = columns[1]
x_cols = columns[2:length(columns)]
formula = build_lm_formula(x_cols, y_cols)
formula
# output
# "`y` ~ `x1` + `x2` + `x3`"

# Run Model
lm(formula = formula, data = df)
# output
Call:
    lm(formula = formula, data = df)

Coefficients:
    (Intercept)           x1           x2           x3  
        -5.6316       0.7895       1.1579           NA  

```

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