Short Answer 
The response explains proportional relationships, characterized by the equation y = kx, where k represents the constant proportionality. It identifies two specific proportions: y = 0.8x, which is graphed in quadrants I and III, and y = -0.4x, found in quadrants II and IV, derived by eliminating constants from their respective equations.
Step 1: Understanding Proportional Relationships
A proportional relationship between two variables, x and y, can be expressed in the form y = kx, where k is the constant of proportionality. In this equation, the slope m of the line is equal to k. This means that whenever you have a line through the origin (0,0), it indicates a direct proportion between the two variables.
Step 2: Identifying the First Proportion
The first direct proportion given is y = 0.8x. This comes from analyzing the equation y = 0.8x – 1.6 and recognizing that removing the constant results in the proportional equation. The slope here is 0.8, and this line is graphed in quadrants I and III, where both x and y are positive, or both are negative.
Step 3: Identifying the Second Proportion
The second direct proportion is y = -0.4x. This derives from the relationship expressed as y = -0.4x + 1. Again, by removing the constant, we can focus on the slope, which is -0.4. The graph of this line exists in quadrants II and IV, where x is negative and y is positive, or vice versa.