Which of the following is a linear function?(1 point)

Question

Responses

y=2x3+4
y equals 2 x cubed plus 4

2y−5x=9
2 y minus 5 x equals 9

y=−12x+78, x≠0
y equals negative Start Fraction 12 over x End Fraction plus Start Fraction 7 over 8 End Fraction comma x is not equal to 0

x2+y=33

Answer 1

A linear function can be represented in the form \(y = mx + b\), where \(m\) and \(b\) are constants, and the graph of the function is a straight line.

Let's analyze the given options:

1. \(y = 2x^3 + 4\): This is a cubic function, not linear.

2. \(2y - 5x = 9\): This can be rearranged into the form \(y = \frac{5}{2}x + \frac{9}{2}\), which is linear.

3. \(y = -12x + 78, x \neq 0\): This is already in the linear form \(y = mx + b\), where \(m = -12\) and \(b = 78\).

4. \(x^2 + y = 33\): Rearranging gives \(y = 33 - x^2\), which is a quadratic function and not linear.

So, the options that are linear functions are \(2y - 5x = 9\) and \(y = -12x + 78\).