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. $y=-12x+78,x\ne 0$: 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 $y=-12x+78$.