Question

which three equations represent non-proportional relationships?

y = 10x + 10

y = 4.08x

y = -15x

y = 5/x-9

y = 2/3x

y = x squared

Answer 1

To identify non-proportional relationships from the given equations, we should look for equations that do not pass through the origin (0,0) or have a constant ratio between \(y\) and \(x\). Proportional relationships are of the form \(y = kx\) where \(k\) is a constant, and these relationships will always pass through the origin. Here are the given equations evaluated:

1. **\(y = 10x + 10\)**: This is a linear equation with a y-intercept of 10, meaning it does not pass through the origin. **(Non-proportional)**

2. **\(y = 4.08x\)**: This is in the form \(y = kx\) where \(k = 4.08\). This passes through the origin. **(Proportional)**

3. **\(y = -15x\)**: This is also in the form \(y = kx\) where \(k = -15\). This passes through the origin. **(Proportional)**

4. **\(y = 5/x - 9\)**: This is a rational function that does not represent a constant ratio between \(y\) and \(x\). It does not pass through the origin. **(Non-proportional)**

5. **\(y = \frac{2}{3}x\)**: This is also in the form \(y = kx\) where \(k = \frac{2}{3}\). This passes through the origin. **(Proportional)**

6. **\(y = x^2\)**: This is a quadratic function and does not represent a constant ratio. It does not pass through the origin (since if \(x = 0\), \(y = 0^2 = 0\), but the proportionality does not hold for other values); hence, it is non-proportional. **(Non-proportional)**

Based on the analysis, the three equations that represent non-proportional relationships are:

1. \(y = 10x + 10\)
2. \(y = \frac{5}{x} - 9\)
3. \(y = x^2\)