Question

Identify which of the following functions is proportional.(1 point)
Responses

y=x+12
y
=
x
+
1
2
y equals x plus Start Fraction 1 over 2 End Fraction

y=12x
y
=
1
2
x
y equals Start Fraction 1 over 2 x End Fraction

y=x2
y
=
x
2
y equals x squared

y=12x

Answer 1

A function is proportional if it can be expressed in the form \( y = kx \), where \( k \) is a constant. This means that the function passes through the origin (0,0) and maintains a constant ratio between \( y \) and \( x \).

Let's evaluate the given options:

1. **\( y = x + 12 \)**: This is not proportional because it does not pass through the origin; at \( x = 0 \), \( y = 12 \).

2. **\( y = x + \frac{1}{2} \)**: This is not proportional for the same reason; at \( x = 0 \), \( y = \frac{1}{2} \).

3. **\( y = 12x \)**: This is proportional because it can be written in the form \( y = kx \) with \( k = 12 \) and passes through the origin.

4. **\( y = \frac{1}{2} x \)**: This is also proportional in the form \( y = kx \) where \( k = \frac{1}{2} \) and also passes through the origin.

5. **\( y = x^2 \)**: This is not proportional because it does not pass through the origin in a linear fashion; at \( x = 0 \), \( y = 0 \) but it does not maintain a constant ratio.

Based on this analysis, the functions that are proportional are:

- \( y = 12x \)
- \( y = \frac{1}{2} x \)

So, the answer is **\( y = 12x \)** and **\( y = \frac{1}{2} x \)**.