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

Question

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?

Answer 1

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 & 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".


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Answer 2

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

Answer 3

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.

Answer 4

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.

Answer 5

You're okay as far as you went, but it's not clear what you're trying to solve for. solve for y ? 8x - 3y = 12 -3y = 12 - 8x 3y = 8x - 12 y = 8/3 x - 4