The fractions of -42/-45 and 14/15 are equivalent
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comparing the relation given
thus y= -2x +1 to the general equation of a line
where y= mx + c
where m is the gradient and c is the intercept on the y-axis.
from the question, the gradient is -2 and since the line is perpendicular, the gradient is given as
so substituting the value of m in to the equation
=
as the gradient
equation of line is given by
y - y1 = m( x-x1)
from the question y1= -2 and x1=1
substitute them
y-(-2) = 1/2 (x -1)
y+2 =1/2 (x-1)
multiplying through by 2
2 (y+2) = x-1
2y +4 = x-1
2y =x-1-4
2y =x-5
x -2y -5 = 0
therefore the equation for the line is x-2y -5=0
Solution: Yes, the random variable y will have a binomial distribution. Because there are two possible outcomes 1. number of days of rain and 2. number of days of no rain.
The parameters of binomial distribution are and
The parameter n is given as the number of day's under consideration.
The parameter p is not given, but it can be estimated by number of days it rained divided by the total number of days under consideration.