19. %0D%0A%0D%0A%0D%0A%0D%0A %0D%0A%0D%0Aa. Using the graph, describe the key characteristics of the graph (positive/negative slope, proportional/non proportional, y-intercept).%0D%0A%0D%0Ab. Write in words what the slope of the graph means in context.%0D%0A%0D%0Ac. Write in words what the y-intercept of the graph means in context.%0D%0A%0D%0Ad. Write in words what the graph of the line is showing.%0D%0A%0D%0A(5 points
a. From the graph, it can be observed that the slope is negative. The graph shows a non-proportional relationship as the line does not pass through the origin. The y-intercept is the point where the line intersects the y-axis.
b. The slope of the graph represents the rate of change in the context of the problem. It indicates the amount by which the dependent variable changes for every unit change in the independent variable.
c. The y-intercept of the graph represents the value of the dependent variable when the independent variable is equal to zero. In the context of the problem, it indicates the initial value or starting point.
d. The graph of the line shows the relationship between the independent and dependent variables. It provides a visual representation of how the dependent variable changes with respect to the independent variable.
a. To describe the key characteristics of the graph, we need to analyze its slope, proportionality, and y-intercept.
- Slope: From the graph, we can see that the slope is positive. This means that as the x-values increase, the corresponding y-values also increase. The line is slanting upwards from left to right.
- Proportionality: The graph appears to be proportional. This is because as the x-values increase or decrease by the same amount, the y-values also increase or decrease by a consistent ratio.
- Y-intercept: The y-intercept is the point where the line intersects the y-axis. In the given graph, the y-intercept appears to be non-zero (not at y=0). It represents the value of y when x=0.
b. The slope of the graph represents the rate of change between the variables. In context, it means that as the x-values increase by a certain amount, the corresponding y-values increase by the same proportion. For example, if the slope was 2, it would mean that for every 1 unit increase in x, y increases by 2 units.
c. The y-intercept of the graph represents the value of y when x is equal to zero. In context, it gives us the starting point or initial value of the relationship between the variables. For example, if the y-intercept is 3, it means that when x=0, the value of y is 3.
d. The graph of the line is showing the relationship between the variables x and y. It indicates how changes in x are related to changes in y. The line provides a visual representation of this relationship, showing the trend and direction of the relationship.