[Linear] Function, Help; Ax+By=C?

Hello guys,





Well, functions have me completely stumped. I am currently bluffing my way through Algebra I (advanced, 8th grade =/), and we hit functions yesterday - they have me completely stumped.





Specifically linear functions. It goes without saying (right?) that exponents, variables/constants in fractions, multiplying y and x, etc. disqualify them as linear functions, correct?





Regardless - I need help.





4y-2x=0





"Tell whether each function is linear. If so, graph the function."





So basically, I know it is linear, and I know how to graph - where do I go from there? The Algebra I teacher is a cool guy, he got us started on y=mx-b a long time ago, but I never under stood. I THINK I have to get y on its own, just like any equation's variable.





So would it be





y-1/2x=0? Where would I go from there?





/dying





By the way - why use (f)x, instead of y? I never understood - in some later stage of math, do the extra variables help you plug in factors and what not?

[Linear] Function, Help; Ax+By=C?
hi...





you seem to know your algebraic processes ... at least... so it still counts...





Ax + By + C = 0 is called the standard form or the general form of the linear equation. A, B %26amp; C are fixed constants...





so you know how to transform it...so that y has a coefficient of 1...





4y - 2x = 0


you now have... y - 1/2 x = 0


you just need to transpose the second term..


y = 1/2 x ...... (this is now called the slope-intercept form of the line) ... it has the form y = mx + b





thus in your example... m = 1/2 is the slope


b = 0 is the y-intercept...








Regarding the other notation...


y = mx + b ...


it is still the same as f(x) = mx + b ... this is just another way of writing the function... f(x) and y are totally interchangeable...


this is just one way of writing the function so that it will be clear that the independent variable is x.





btw... i know you know that that notation is NOT 'f multiplied to x'.


you read that as... "f of x".








§
Reply:Move the x to the RHS


y = 1/2x. And done.





By the way - why use (f)x, instead of y? I never understood - in some later stage of math, do the extra variables help you plug in factors and what not?


—Something like that, yes. Just wait.
Reply:from y - (1/2)x = 0, add (1/2)x to both sides, getting y = (1/2)x, which of course is linear, y = mx + b with m = 1/2 and b = 0.





f(x) makes you think of the result of doing stuff to x to get y, the stuff you do is what the function rule describes. Just think of the f(x) as y.
Reply:okay have y by itself on one side of the equation to put it in slope-intercept form:





y= 1/2x





To graph you would look for a y intercept (the b ) which is zero here. y=m(slope)x + b(y-intercept)





so put a point on the graph at the origin to mark the y-int.


Then the slope is rise/run. which means rise 1 unit and run horizontally to the right 2





in other words up 1 over 2 and you have your graph. repeat the whole up 1 over 2 thing until your graph runs out. or go negatively by down one left 2 (just the opposite) that will give you the same thing





hope this helps!





and you will use f(x) because y is actually a function of x. so they shorten it to f(x) and it will make complete sense when you move through math classes

magnolia