Question

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

x2+y=33

x squared plus y is equal to 33

2y−5x=9

2 y minus 5 x is equal to 9

y=2x3+4

y is equal to 2 x cubed plus 4

y=−12x + 78, x≠0

Answer 1

A linear function has variables only to the first power and can be written y = mx + b (or ax + by = c).

Check each:
- x^2 + y = 33 → y = 33 − x^2 (quadratic) → not linear.
- 2y − 5x = 9 → y = (5/2)x + 9/2 → linear.
- y = 2x^3 + 4 → cubic → not linear.
- y = −12x + 78, x ≠ 0 → linear (degree 1); the domain restriction doesn’t change its linear form.

So the linear ones are 2y − 5x = 9 and y = −12x + 78. If only one choice is allowed, pick 2y − 5x = 9.