#Problem 1

#definition of a straight line function
y=function(x,m,b) m*x+b

#definition x-Vctor
x_vec=seq(-1,3,0.1)

#definition y-vector
y_vec=array(0,dim=c(length(x_vec)))
for (i in (0:length(x_vec))){
            y_vec[i]=y(x_vec[i],1,0)
}
#plotting x-vector vs. y-vector
plot(x_vec, y_vec, type="l", col="black", xlab='x',ylab='f(x)=y')

#generating mock data point for 0 <= x <= 2 for 10 equaly spaced points
equ_points=10
x_vec_2=seq(0,2, 2/(equ_points-1))
for (i in x_vec_2){
    points(i,rnorm(1, sd =  0.4), col="red", type="p")
}