Which linear equation shows a proportional relationship?

Question

y = 4
y equals one half times x
y = 2x + 3
y equals negative three halves times x minus 1

Answer 1

A proportional relationship is described by a linear equation of the form \( y = kx \), where \( k \) is a constant and there is no y-intercept (i.e., the line passes through the origin).

Considering the equations you provided:

1. \( y = 4 \) - This is a horizontal line (constant value), not proportional.
2. \( y = \frac{1}{2}x \) - This is in the form \( y = kx \), which is proportional with \( k = \frac{1}{2} \).
3. \( y = 2x + 3 \) - This has a y-intercept of 3, so it is not proportional.
4. \( y = -\frac{3}{2}x - 1 \) - This has a y-intercept of -1, so it is not proportional.

The equation that shows a proportional relationship is:

\( y = \frac{1}{2}x \).