Question

1. which graph or table shows the proportional relationship described by the function $y = -2x$?

a
graph a: a line passing through the origin with a positive slope
b
graph b: a line passing through the origin with a negative slope
c

x	y
4	-4
6	-6

d
table d (partially shown): x and y columns

Explanation:

Step1: Recall properties of \( y = -2x \)

The function \( y = -2x \) is a proportional relationship (passes through the origin, \( y = kx \) with \( k = -2 \)). The slope \( k = -2 \) is negative, so the line should decrease from left to right.

Step2: Analyze Graph A

Graph A has a positive slope (increases from left to right), so it can't represent \( y = -2x \) (slope -2 is negative). Eliminate A.

Step3: Analyze Graph B

Graph B passes through the origin and has a negative slope (decreases from left to right), matching \( y = -2x \) (slope -2). Check further.

Step4: Analyze Table C

For \( y = -2x \), when \( x = 2 \), \( y = -2(2) = -4 \), but table C has \( y = -2 \) for \( x = 2 \). Doesn't match. Eliminate C.
(Assuming D is inconsistent, but focus on B as it matches slope and origin.)

Answer:

B. The graph in option B