Is this a function?

Question

Is 2x +3y = 4 a function?

Justify.

Answer 1

Yes, this is a function. You can isolate y to get y=(4-2x)/3.
This could be rewritten as f(x)=(4-2x)/3.
For every x value that you put in, you get a y value.
You could also rewrite it as x=(4-2y)/2, in which case you could have f(y)=(4-2y)/2.
For every y value that you put in, you get an x value.
This constitutes a function.

Answer 2

Yes...it specifies the resulting dependent variable's value with the given independent variable's value.

This is the essence of the mathematical concept of a function. More below.

In this case, either can be the dependent and independent variables, but y is usually the dependent variable.

Answer 3

yes this is in standard form of a line and a line never has 2 of the same x values with one y so it is a function

Answer 4

well, if you put it in slope intercept form

2x+3y=4
3y=-2x+4
y=-2/3x+4/3

which defines a line, and nonvertical lines are indeed functions, so yes!

Answer 5

yes, it is a line of the form

y= -(2/3)*x + (4/3)

-or-

y= m*x+b

justify-
continuous,
only one value of y for every x.

Answer 6

Yes, since you can isolate the x and y terms such that you form equations
x = by+c or y = fx+g.