Question
which functions are linear
y = x - 2
y = 3/x + 2
y = 1/2x + 8
y = 2x - 4
y = 8x^2 - 2
y = x - 2
y = 3/x + 2
y = 1/2x + 8
y = 2x - 4
y = 8x^2 - 2
Answers
GPT-4o mini
A linear function can be expressed in the form \(y = mx + b\), where \(m\) and \(b\) are constants. Let's analyze each of the given functions to see which are linear:
1. **\(y = x - 2\)**: This is in the form \(y = mx + b\) with \(m = 1\) and \(b = -2\). **This is a linear function.**
2. **\(y = \frac{3}{x} + 2\)**: This is not in the linear form, as it contains a term \(\frac{3}{x}\), which is not linear. **This is not a linear function.**
3. **\(y = \frac{1}{2}x + 8\)**: This is in the form \(y = mx + b\) with \(m = \frac{1}{2}\) and \(b = 8\). **This is a linear function.**
4. **\(y = 2x - 4\)**: This is in the form \(y = mx + b\) with \(m = 2\) and \(b = -4\). **This is a linear function.**
5. **\(y = 8x^2 - 2\)**: This function contains the term \(8x^2\), which means it is quadratic rather than linear. **This is not a linear function.**
In summary, the linear functions from your list are:
- \(y = x - 2\)
- \(y = \frac{1}{2}x + 8\)
- \(y = 2x - 4\)
1. **\(y = x - 2\)**: This is in the form \(y = mx + b\) with \(m = 1\) and \(b = -2\). **This is a linear function.**
2. **\(y = \frac{3}{x} + 2\)**: This is not in the linear form, as it contains a term \(\frac{3}{x}\), which is not linear. **This is not a linear function.**
3. **\(y = \frac{1}{2}x + 8\)**: This is in the form \(y = mx + b\) with \(m = \frac{1}{2}\) and \(b = 8\). **This is a linear function.**
4. **\(y = 2x - 4\)**: This is in the form \(y = mx + b\) with \(m = 2\) and \(b = -4\). **This is a linear function.**
5. **\(y = 8x^2 - 2\)**: This function contains the term \(8x^2\), which means it is quadratic rather than linear. **This is not a linear function.**
In summary, the linear functions from your list are:
- \(y = x - 2\)
- \(y = \frac{1}{2}x + 8\)
- \(y = 2x - 4\)