19. a. Using the graph, describe the key characteristics of the graph (positive/negative slope, proportional/non proportional, y-intercept). b. Write in words what the slope of the graph means in context. c. Write in words what the y-intercept of the graph means in context. d. Write in words what the graph of the line is showing. (5 points)
Without the graph, it is not possible to answer these questions. Please provide the graph.
a. To describe the key characteristics of the graph, we need to analyze its slope, proportionality, and y-intercept.
1. Slope: To determine the slope of the graph, observe the direction of the line. If the line moves from left to right and rises as it moves, the slope is positive. Conversely, if the line moves from left to right and falls as it moves, the slope is negative.
2. Proportionality: Consider if the graph represents a proportional relationship between the x-axis and the y-axis. If the graph displays a straight line passing through the origin (0,0), it indicates a proportional relationship. On the other hand, if the line does not pass through the origin, it signifies a non-proportional relationship.
3. Y-intercept: Identify the point at which the graph intersects the y-axis (the vertical axis). This is known as the y-intercept. The y-intercept represents the value of the dependent variable (usually denoted as y) when the independent variable (usually denoted as x) is zero.
b. To explain the meaning of the slope in context, consider the variables represented on the axes of the graph. Let's assume the vertical axis represents the dependent variable (y), and the horizontal axis represents the independent variable (x). The slope can be interpreted as the rate of change, or the amount by which the dependent variable changes for every unit change in the independent variable. For example, if the slope is positive, it implies that as x increases, y also increases. Conversely, a negative slope indicates that as x increases, y decreases.
c. The y-intercept of the graph represents the value of the dependent variable (y) when the independent variable (x) is zero. In practical terms, the y-intercept provides a starting point or baseline value for the dependent variable. For instance, if the graph represents a distance-time relationship, the y-intercept could indicate the initial distance traveled at time zero.
d. The graph of the line shows the relationship between the two variables, represented by the x- and y-axes. It visualizes how the dependent variable (y) changes concerning the independent variable (x), whether it is proportional or non-proportional, positive or negative, and provides insight into the starting point or baseline value of the dependent variable.
a. Based on the graph, we can observe that the slope of the line is positive. It indicates that the graph has a positive slope.
The graph appears to be proportional because the line passes through the origin and the points seem to lie on a straight line.
Additionally, we can determine that the y-intercept is 0 since the line passes through the origin (0,0).
b. The slope of the graph represents the rate of change between the two variables in context. It indicates how much the dependent variable (y-axis) changes for each unit increase in the independent variable (x-axis). In other words, it shows the constant rate at which the values of y increase as x increases.
c. The y-intercept of the graph represents the value of the dependent variable (y-axis) when the independent variable (x-axis) is equal to zero. In context, it signifies the initial or starting value of the dependent variable. In this case, since the y-intercept is at (0,0), it means the value of y is zero when x is also zero.
d. The graph of the line shows a proportional relationship between two variables. It demonstrates that as the independent variable (x-axis) increases, the dependent variable (y-axis) also increases at a constant rate. The line passes through the origin, indicating that when x is zero, y is also zero, supporting the proportional nature of the relationship between the two variables.