Question

Which of the following is a linear function?(1 point) Responses x2+y=33 x squared plus y equals 33 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

Answer 1

To identify which of the given equations represents a linear function, we should look for equations that can be expressed in the form \( y = mx + b \), where \( m \) and \( b \) are constants.

Let's analyze each option:

1. **\( x^2 + y = 33 \)**: This can be rewritten as \( y = 33 - x^2 \), which is not linear due to the \( x^2 \) term.

2. **\( y = -12x + 78, x \neq 0 \)**: This is already in the form \( y = mx + b \) with \( m = -12 \) and \( b = 78\). This is a linear function.

3. **\( y = -\frac{12}{x} + \frac{7}{8}, x \neq 0 \)**: This is not linear; the term \(-\frac{12}{x}\) indicates a hyperbola.

4. **\( y = 2x^3 + 4 \)**: This contains the \( x^3 \) term, making it a cubic function, not linear.

5. **\( 2y - 5x = 9 \)**: We can rewrite this as \( y = \frac{5}{2}x + \frac{9}{2} \), which is in the linear form again.

Based on this analysis, the equations that represent linear functions are:

- \( y = -12x + 78 \)
- \( 2y - 5x = 9 \) (when rewritten as \( y = \frac{5}{2}x + \frac{9}{2} \))

Therefore, the correct response indicating a linear function is either **\( y = -12x + 78 \)** or **\( 2y - 5x = 9 \)**.