# The line joining two distinct 2D points `a` and `b` An object of class `"Lines"`. Returns the `equation, slope, intercept`, and $y$-coordinates of the line crossing two distinct 2D points `a` and `b` with $x$-coordinates provided in `vector` `x`. This function is different from the `line` function in the standard `stats` package in `R` in the sense that `Line(a,b,x)` fits the line passing through points `a` and `b` and returns various quantities (see below) for this line and `x` is the $x$-coordinates of the points we want to find on the `Line(a,b,x)` while `line(a,b)` fits the line robustly whose $x$-coordinates are in `a` and $y$-coordinates are in `b`. `Line(a,b,x)` and `line(x,Line(A,B,x)$y)` would yield the same straight line (i.e., the line with the same coefficients.) ```r Line(a, b, x) ``` ## Arguments - `a, b`: 2D points that determine the straight line (i.e., through which the straight line passes). - `x`: A scalar or a `vector` of scalars representing the $x$-coordinates of the line. ## Returns A `list` with the elements - **desc**: A description of the line - **mtitle**: The `"main"` title for the plot of the line - **points**: The input points `a` and `b` through which the straight line passes (stacked row-wise, i.e., row 1 is point `a` and row 2 is point `b`). - **x**: The input scalar or `vector` which constitutes the $x$-coordinates of the point(s) of interest on the line. - **y**: The output scalar or `vector` which constitutes the $y$-coordinates of the point(s) of interest on the line. If `x` is a scalar, then `y` will be a scalar and if `x` is a `vector` of scalars, then `y` will be a `vector` of scalars. - **slope**: Slope of the line, `Inf` is allowed, passing through points `a` and `b` - **intercept**: Intercept of the line passing through points `a` and `b` - **equation**: Equation of the line passing through points `a` and `b` ## Examples ```r A<-c(-1.22,-2.33); B<-c(2.55,3.75) xr<-range(A,B); xf<-(xr[2]-xr[1])*.1 #how far to go at the lower and upper ends in the x-coordinate x<-seq(xr[1]-xf,xr[2]+xf,l=5) #try also l=10, 20, or 100 lnAB<-Line(A,B,x) lnAB summary(lnAB) plot(lnAB) line(A,B) #this takes vector A as the x points and vector B as the y points and fits the line #for example, try x=runif(100); y=x+(runif(100,-.05,.05)) plot(x,y) line(x,y) x<-lnAB$x y<-lnAB$y Xlim<-range(x,A,B) if (!is.na(y[1])) {Ylim<-range(y,A,B)} else {Ylim<-range(A,B)} xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] pf<-c(xd,-yd)*.025 #plot of the line joining A and B plot(rbind(A,B),pch=1,xlab="x",ylab="y", xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) if (!is.na(y[1])) {lines(x,y,lty=1)} else {abline(v=A[1])} text(rbind(A+pf,B+pf),c("A","B")) int<-round(lnAB$intercep,2) #intercept sl<-round(lnAB$slope,2) #slope text(rbind((A+B)/2+pf*3),ifelse(is.na(int),paste("x=",A[1]), ifelse(sl==0,paste("y=",int), ifelse(sl==1,ifelse(sign(int)<0,paste("y=x",int),paste("y=x+",int)), ifelse(sign(int)<0,paste("y=",sl,"x",int),paste("y=",sl,"x+",int)))))) ``` ## See Also `slope`, `paraline`, `perpline`, `line` in the generic `stats` package and and `Line3D` ## Author(s) Elvan Ceyhan

Line function