Question

Which THREE equations represent non-proportional relationships?(1 point)
Responses

y=23x
y is equal to 2 thirds x

y=x2
y is equal to x squared

y=4.08x
y is equal to 4 point 0 8 x

y=5x−9
y is equal to the fraction with numerator 5 and denominator x minus 9

y=−15x
y is equal to negative 15 x

y=10x+10

Answer 1

To determine which equations represent non-proportional relationships, we can look for the presence of a constant term (other than zero) in the equations. Non-proportional relationships cannot be expressed in the form \( y = kx \), where \( k \) is a constant.

Here are the equations you provided:

1. \( y = 23x \) - Proportional
2. \( y = \frac{2}{3} x \) - Proportional
3. \( y = x^2 \) - Non-proportional (this is a quadratic relationship)
4. \( y = \frac{5}{x} - 9 \) - Non-proportional (this involves a variable in the denominator and a constant)
5. \( y = -15x \) - Proportional
6. \( y = 10x + 10 \) - Non-proportional (due to the constant term +10)

From this analysis, the three equations that represent non-proportional relationships are:

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

Thus, the answers are \( y = x^2 \), \( y = \frac{5}{x} - 9 \), and \( y = 10x + 10 \).