Linear equation - Wikipedia, the free encyclopedia
You have it in a y=mx+b form (y-axis form). Basically, if you know the slope, m, and a point on the line (x0,y0), then you can immediately write the equation of the line in the point slope form:
y-y0 = m(x-x0)
for this example:
m = (45-5)/(2000-1980) = 40/20 = 2 (which you already got)
And it needs to go through both of those points. Just pick one:
y-5 = 2 * (x-1980)
You would get the same line if you had picked the other point, but it would just look different in this form. IF you were to convert both to y-axis forms (y=mx+b) by just simplifying, you would see they are the same.
I assume you mean f(x) = 214.3x-415368?
This is just function notation. This is the same thing as saying if y = 214.3x-415368 then find y if x = 1980.
When you say f(x), you say there is some formula out there that depends on x. So they are saying the number of radio stations is denoted by the function f. f(x) means evaluate that formula (if possible) at x. The parentheses here mean something different then we normally use them in algebra. Normally we are grouping expressions together like 3(x+1). When we put them next to a function, we mean here is the argument list. So if f(x) = x^2+2, and they say what is f(4), this means replace every occurance of x with 4: f(4) = (4)^2+2= 18.
So to come back to reality: they are just asking, if f(x), given by the formula f(x) = 214.3x-415368, is the number of radio stations on the air from 1950 to 1995 where x is the year, find out how many radio stations were on the air in 1980. i.e. find f(1980).
As for the other two questions, notice that f(x) is a line (think of f(x) as y). If I asked the same question but gave you y = 214.3x-415368 do you see it?