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

Question

Responses

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

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

2y−5x=9
2 y minus 5 x equals 9

x2+y=33

Answer 1

To determine which of the given equations is a linear function, we can evaluate each one:

1. $y=-12x+78$: This is in the form $y=mx+b$, where $m=-12$ and $b=78$. This is a linear function.

2. $y=-\frac{12}{x}+\frac{7}{8}$: This equation involves $\frac{1}{x}$, which means it's not linear (it is a rational function).

3. $y=2x^3+4$: This involves $x^3$, which indicates it is a cubic function, not linear.

4. $2y-5x=9$: We can rearrange this into the form $y=mx+b$: $$2y=5x+9y=\frac{5}{2}x+\frac{9}{2}$$ This is also a linear function.

5. $x^2+y=33$: This involves $x^2$, which indicates it is a quadratic function, not linear.

Thus, the options that represent linear functions are:

• $y=-12x+78$
• $2y-5x=9$ (which can be rearranged to a linear form)

Final Response: Both $y=-12x+78$ and $2y-5x=9$ are linear functions.