Question

Which equation represents a proportional​ relationship?
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Part 1
A.
y​ = negative 2 x ​- 5
B.
y​ = negative 2 x
C.
y​ = 5​ - negative 2 x
D.
y​ = negative 2 x ​+ 5

Answer 1

A proportional relationship is characterized by a direct relationship between two variables, meaning that one variable is a constant multiple of the other, and it can be represented by the equation of the form \( y = kx \), where \( k \) is a constant and \( y \) and \( x \) pass through the origin (0, 0).

Let's examine each of the given equations:

A. \( y = -2x - 5 \)
- This is not proportional, as it has a y-intercept of -5.

B. \( y = -2x \)
- This is proportional. It has the form \( y = kx \) with \( k = -2 \) and passes through the origin.

C. \( y = 5 - 2x \)
- This is not proportional, as it can be rearranged to show it has a y-intercept of 5.

D. \( y = -2x + 5 \)
- This is not proportional, as it has a y-intercept of 5.

The equation that represents a proportional relationship is:

**B. \( y = -2x \)**.