Determine whether the equation defines y as a linear function of x. If so, write it in the form
y = mx + b.
6x-9y^2+8=0
a. y=6x+8
b. y=6/9x-8
c. y=6x-8
d. y=6/9x+8
e. y= y is not a linear function on x
Thank you for your help.
parabola, not a line, because y is squared
To determine whether the equation defines y as a linear function of x, we need to rewrite the equation in the form y = mx + b.
Given equation: 6x - 9y^2 + 8 = 0
Step 1: Isolate the term containing y by moving all other terms to the other side of the equation.
6x + 8 = 9y^2
Step 2: Divide both sides of the equation by 9 to solve for y^2.
(6x + 8) / 9 = y^2
Step 3: Take the square root of both sides to solve for y.
√[(6x + 8) / 9] = y
Now, we have the equation in the form y = mx + b. However, it is important to note that this equation is not linear because it contains the term y^2, which makes it a quadratic equation.
Therefore, the correct option is e. y is not a linear function of x.