SOLUTION: determine whether the equation defines y as a function of x X2+6y=4

Algebra.Com
Question 1095903: determine whether the equation defines y as a function of x

X2+6y=4

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
start with x^2 + 6y = 4

subtract x^2 from both sides of this equation to get:

6y = 4 - x^2

divide both sides of this eqaution by 6 to get:

y = (4 - x^2) / 6

offhand i would say yes because there is only one value of y for each and every value of x.

for example, assume that x = 2.

y = (4-4) / 6 which is equal to 0.

assume that x = -2.

y = (4-4) / 6 which is equal to 0.

you have the same value of y for two different values of x, but you don't have the same value of x for two different values of y, therefore y is a function of x.

the graph will show this to be true.

that graph is shown below:

give the graph the vertical line test and you will see that there is only one value of y for each and every value of x.

$$$


RELATED QUESTIONS

determine whether the equation defines y as a function of x y=x2 and... (answered by MathLover1)
determine whether the equation defines y as a function of x. x2(SQUARE) +... (answered by Fombitz)
Determine whether the following equation defines y as a function of x: x2 + y = 16 (answered by t0hierry)
Determine whether the equation defines y as a function of x. x2 + y = 25 (answered by Theo)
Determine whether the equation defines y as a function of x. x2 + y2 = 1 (answered by jim_thompson5910)
Determine whether the equation defines y as a function of x. xy + 6y = 1 (answered by MathLover1)
Determine whether the equation defines y as a function of x.... (answered by Fombitz)
Determine whether the equation defines y as a function of x: y = 2xsquared -3x + 4 (answered by stanbon)
Determine whether the equation defines y as a function of x. x + y = 9 (answered by jim_thompson5910)