Final answer:
The equation 'y = 0.2x + 500' has a positive slope of 0.2, which means the house price increases by $200 for every additional square foot. The y-intercept is 500, indicating the base price of the house at $500,000. It models a linear relationship between the size of the house and its price.
Step-by-step explanation:
When analyzing the equation y = 0.2x + 500, we can determine several characteristics that describe the relationship between the size of a house and its price. Here, the coefficient '0.2' represents the slope of the line, which indicates the rate at which the price of the house (y) changes with respect to its size in square feet (x). Specifically, for each additional square foot, the price of the house increases by $200. This means that the slope is positive, reflecting a direct relationship where as the size of the house increases, the price also increases. On the other hand, the term '500' represents the y-intercept, which is the base price of the house when the size is zero square feet. Thus, even if a house has no size, it would still cost $500,000 due to other factors included in the base price.
We can also address some misinterpretations: a positive slope does not indicate a decrease in house price with an increase in size, as stated in option a). Instead, it signifies an increase in house price. Additionally, this equation does not model an exponential relationship as suggested in option c); it models a linear relationship since the change in y for each unit change in x is constant, and the graph of the equation is a straight line.