Question

1. the scatter diagram shows the number of sales of hot - chocolate a cafe makes as a function of

3a which type of model would be appropriate for this data?
the correct option was a
linear a
quadratic

3b will the slope of the line in the linear model be positive or negative?
positive a
negative b

Explanation:

3b

The problem is about the slope of a linear model for hot - chocolate sales. Generally, as a relevant factor (like temperature decreasing, or a factor that leads to more hot - chocolate consumption increasing) changes, if the number of hot - chocolate sales increases with a change in the independent variable (for example, as temperature gets colder, hot - chocolate sales go up), the slope would be related to the direction of the relationship. In the context of hot - chocolate sales, typically, as a variable like temperature decreases (or another factor that promotes hot - chocolate sales increases), the number of hot - chocolate sales increases. So the relationship between the independent variable (say, temperature) and the number of sales (dependent variable) would have a negative slope? Wait, no, wait. Wait, maybe the independent variable is something like time (but no, more likely, if it's a factor like temperature: as temperature decreases, hot - chocolate sales increase. So if we plot sales vs. temperature, the slope would be negative? But wait, maybe the independent variable is something else. Wait, the original problem is about hot - chocolate sales as a function of some variable (probably a variable like temperature, where lower temperature leads to more sales). So if we have sales (y) and the variable (x, say temperature), as x (temperature) increases, y (sales) decreases. So the slope (m in y = mx + b) would be negative? Wait, no, wait, maybe I got it wrong. Wait, no, let's think again. If the linear model is for hot - chocolate sales, and the independent variable is something like the number of cold days, or temperature (lower temperature means more sales). So if x is temperature (higher x is warmer), then as x increases, y (sales) decreases. So the slope would be negative? Wait, but maybe the independent variable is something else. Wait, the question is about the slope of the linear model for hot - chocolate sales. Let's recall that slope is (change in y)/(change in x). If, for example, as the independent variable (let's say, the variable on the x - axis) increases, the number of hot - chocolate sales (y - axis) increases, then slope is positive. But in reality, for hot - chocolate, as temperature (a common variable) increases, hot - chocolate sales decrease. So if x is temperature (increasing x means warmer), then y (sales) decreases. So (change in y) is negative when (change in x) is positive, so slope is negative? Wait, no, wait, maybe the independent variable is not temperature. Wait, the problem says "the number of sales of hot - chocolate a cafe makes as a function of" (the rest is cut off). But typically, for hot - chocolate sales, as a variable like the outside temperature decreases, sales increase. So if we model sales (y) as a function of temperature (x), then as x increases (warmer), y decreases. So the slope (m) in y = mx + b would be negative? Wait, but maybe the independent variable is something else, like the number of customers, but that's less likely. Wait, no, maybe I made a mistake. Wait, let's think about the general case. If the linear model has a positive slope, that means as x increases, y increases. If negative, as x increases, y decreases. For hot - chocolate sales, if the independent variable is a variable that is associated with colder weather (like, for example, the number of degrees below a certain temperature), then as that variable increases, sales increase, so slope is positive. But if the independent variable is temperature (in degrees), then as temperature increases, sales decrease, so slo…

Answer:

B. Negative