Determine whther the equation defines y as a linear function of x. If so, write in the form of y = mx + b. 4x - 7y^2 + 6 = 0

Question

Determine whther the equation defines y as a linear function of x. If so, write in the form of y = mx + b.

4x - 7y^2 + 6 = 0

Answer 1

The equation given to you is

 

4x - 7y² + 6 = 0

 

In a linear function, the value of the exponent in any of the terms variables in the function is no more than 1.  In this equation, we have a term with the exponent of 2.  This indicates that we will have in inverse parabola.  If we solve for y, we obtain

 

-7y² = -4x - 6

 

y = ± √((4/7)x + (6/7))

 

We get a square-root function.  This equation does not match the y=mx+b form because

 

y = mx + b  is not the same as  y = ±√(mx + b).