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 \( y = mx + b \): \[ 2y = 5x + 9 \ y = \frac{5}{2}x + \frac{9}{2} \] 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.