To provide accurate answers to your questions, I would need to have visibility of the graph you're referring to. However, I can outline how you would typically answer these questions based on any graph representing a linear relationship:
a) Is this a proportional relationship?
Answer: A relationship is proportional if it can be written as \( y = kx \), where \( k \) is a constant and \( y \) is zero when \( x \) is zero (the graph passes through the origin). If the graph does not pass through the origin, it is not proportional.
b) What is the y-intercept?
Answer: The y-intercept is the value of \( y \) when \( x = 0 \). You can determine this by locating the point where the line crosses the y-axis.
c) What does the y-intercept mean in the context of the scenario?
Answer: The y-intercept represents the value of \( y \) in the scenario when the \( x \)-variable is zero. It often indicates the starting point or initial value of the context being analyzed.
d) What is the slope?
Answer: The slope (often represented as \( m \)) is the ratio of the rise (change in \( y \)) over the run (change in \( x \)). You can calculate the slope by taking two points on the line and using the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
e) What does the slope mean in the context of the scenario?
Answer: The slope indicates the rate of change of \( y \) concerning \( x \). In terms of the scenario, it illustrates how much \( y \) increases or decreases for each unit increase in \( x \).
If you can provide specifics about the graph, I can give more precise answers tailored to that information.