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 isn't a linear function on x.
Thank you.
You need to solve for y. Do you have any thoughts of what the answer is?
the graph of a linear function is a straight line.
Does y^2 define a straight line?
To determine whether the equation defines y as a linear function of x, we need to rewrite it in the form y = mx + b.
Starting with the equation 6x - 9y^2 + 8 = 0, we can try to isolate y.
First, subtract 6x from both sides:
-9y^2 = -6x - 8
Next, divide both sides by -9 to solve for y^2:
y^2 = (6/9)x + 8/9
Taking the square root of both sides:
y = ±√((6/9)x + 8/9)
Since the equation contains a square root, y is not defined as a linear function of x. Therefore, the answer is e. y isn't a linear function on x.
To determine if the equation defines y as a linear function of x, we need to make sure that the highest power of y is 1 (y^1), and that there are no other terms involving y, such as y^2, y^3, etc.
Let's analyze the equation 6x - 9y^2 + 8 = 0.
Since there is a term (-9y^2), the equation does not define y as a linear function of x.
Therefore, the correct answer is e. y isn't a linear function of x.
To come to this conclusion yourself, you can follow these steps:
1. Determine the highest power of y involved in the equation.
2. If the highest power of y is 1 (y^1) or there are no terms involving y, then the equation represents a linear function of x.
3. If the highest power of y is greater than 1 (y^2, y^3, etc.), then the equation does not represent a linear function of x.