Question

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

y=−1/2x+7/8, 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 options is a linear function, let's analyze each one:

1. **\(y = -\frac{1}{2}x + \frac{7}{8}\)**: This is in the form of \(y = mx + b\), which is the standard form for a linear function. So this is a linear function.

2. **\(y = 2x^3 + 4\)**: This includes the term \(x^3\), which indicates that it is a cubic function, not linear.

3. **\(2y - 5x = 9\)**: This can be rearranged into slope-intercept form \(y = mx + b\). Rearranging gives \(y = \frac{5}{2}x + \frac{9}{2}\), which is linear.

4. **\(x^2 + y = 33\)**: This includes the term \(x^2\), indicating it is a quadratic function, not linear.

Based on this evaluation, the options that are linear functions are:
- \(y = -\frac{1}{2}x + \frac{7}{8}\)
- \(2y - 5x = 9\)

So, both the first and third options represent linear functions.