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Write the equation of the line y=mx through the origin that describes the proportional relationship

A.
y = 1/2x

B.
y = x

C.
y = 2x

1 answer

The equation of a line in the form \( y = mx \) describes a proportional relationship through the origin, where \( m \) is the slope of the line.

  1. Option A: \( y = \frac{1}{2}x \) has a slope of \( \frac{1}{2} \).
  2. Option B: \( y = x \) has a slope of \( 1 \).
  3. Option C: \( y = 2x \) has a slope of \( 2 \).

All three options describe lines through the origin and represent proportional relationships.

To summarize:

  • \( y = \frac{1}{2}x \) reflects a lower proportionality to \( x \).
  • \( y = x \) reflects a one-to-one proportionality to \( x \).
  • \( y = 2x \) reflects a greater proportionality than \( x \).

Thus, all three equations \( y = \frac{1}{2}x \), \( y = x \), and \( y = 2x \) are valid equations for lines that describe proportional relationships through the origin.