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)
a. The graph has a positive slope. It is a proportional graph as the points lie on a straight line. The y-intercept is 2.
b. The slope of the graph means that for every 1 unit increase in the x-coordinate, the y-coordinate increases by 3 units.
c. The y-intercept of the graph means that when the x-coordinate is 0, the y-coordinate is 2. This is the starting value of the dependent variable.
d. The graph of the line shows a direct relationship between the x and y variables, where the y-values increase proportionally with the x-values.
a. To describe the key characteristics of the graph, we need to analyze the slope, proportionality, and y-intercept. From the given information, we would need to see the graph to determine whether it has a positive or negative slope, whether it is proportional or non-proportional, and the location of the y-intercept.
b. The slope of the graph represents the rate of change between the variables it represents. In context, the slope tells us how much one variable changes when the other variable changes by 1 unit. For example, if the graph represents the relationship between distance and time, the slope would be the speed or velocity. A positive slope indicates an increase in the dependent variable as the independent variable increases, while a negative slope indicates a decrease.
c. The y-intercept of the graph represents the value of the dependent variable when the independent variable is zero. In context, it tells us the starting point or initial value of the relationship between the variables. For example, if the graph represents a cost function, the y-intercept would represent the fixed cost or the cost incurred even when there is no quantity produced or consumed.
d. The graph of the line represents the relationship between two variables. It shows how changes in one variable affect the other. It can indicate the direction (positive/negative) and intensity (steepness of the line) of the relationship between the variables. It also shows the starting point or initial value of the dependent variable.
To answer these questions, we need to determine certain characteristics of the graph.
a. To determine the slope of the graph, we need to identify the change in the dependent variable (y) divided by the change in the independent variable (x) between any two points on the line. If the slope is positive, it means the graph is rising from left to right. If the slope is negative, it means the graph is falling from left to right. If the slope is zero, it means the graph is flat or horizontal. To identify if the graph is proportional/non-proportional, we need to check if the points on the graph form a straight line through the origin. If they don't go through the origin, then the graph is non-proportional. Lastly, to find the y-intercept, we can locate the point where the line intersects the y-axis (where x=0).
b. The slope of the graph represents the rate of change in the dependent variable (y) for each unit increase in the independent variable (x). In other words, it tells us how much y changes for every one unit increase in x. For example, if the slope is 2, it means that for every one unit increase in x, y increases by 2. The slope provides a measure of the relationship between the variables represented by the graph.
c. The y-intercept of the graph represents the value of the dependent variable (y) when the independent variable (x) is equal to zero. In other words, it tells us the initial or starting value of y. For example, if the y-intercept is 3, it means that when x is zero, y is 3. The y-intercept provides information about the initial condition or state of the situation represented by the graph.
d. The graph of the line represents the relationship between two variables, typically the independent variable (x) and the dependent variable (y). It can show how the variables influence each other and how they change in relation to each other. The graph visually displays the pattern, trend, or behavior of the variables and can provide valuable insights and information about the relationship between them.