(0,8), (10,15), (20,17), (30,23), (50, 31)
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.
a. The graph has a positive slope because the values of y increase as the values of x increase. It is also proportional because the ratio of y to x remains constant. The y-intercept is not provided, so it cannot be determined from the given points.
b. The slope of the graph represents the rate of change between the x and y values. In this case, for every increase of 10 in x, there is an increase of 7 in y, so the slope is 7/10. This means that for every unit increase in x, the y value increases by 0.7 units.
c. Since the y-intercept is not provided, its meaning cannot be determined from the given points.
d. The graph of the line represents a relationship between x and y, where y increases at a constant rate as x increases.
a. From the given coordinates, we can observe that the graph has a positive slope. This is because as the x-values increase, the corresponding y-values also increase. The graph appears to be proportional, as the increase in x leads to a consistent increase in y. At x=0, the graph does not intersect the y-axis, so it does not have a y-intercept.
b. The slope of the graph represents the rate of change, or the increase in y for each increase in x. In this case, the slope can be calculated by using any two points on the graph. For example, using the points (0,8) and (10,15), we can calculate the slope as (15-8)/(10-0) = 7/10. In context, this means that for every increase of 10 units in x, there is an increase of 7 units in y.
c. Since the graph does not intersect the y-axis, it does not have a y-intercept. In context, this means that the initial value of y is 0 when x=0.
d. The graph of the line represents a relationship between two variables, where the increase in x is associated with an increase in y. It shows the trend or pattern of how these variables are related. In this case, as x increases, y also increases at a consistent rate, indicating a positive linear relationship between the two variables.
a. To determine the characteristics of the graph, we can examine the given data points.
First, let's plot the points on a coordinate plane:
(0,8), (10,15), (20,17), (30,23), (50, 31)
Based on the graph created, we can observe the following key characteristics:
- Slope: The graph appears to have a positive slope. As we move from left to right, the y-values increase.
- Proportional/Non-proportional: The graph shows a general trend where the y-values increase as the x-values increase. However, the relationship between x and y does not follow a simple proportional pattern. It is more complex and may involve other factors not captured by these data points.
- Y-intercept: The graph does not pass through the y-axis at any point before the first given data point. Therefore, it does not have a y-intercept in this context.
b. The slope of the graph represents the rate of change between the x and y values. In this case, since the slope is positive, it means that as the x-values increase, the y-values also increase. The greater the positive slope, the steeper the increase in the y-values for each unit increase in the x-values.
c. The y-intercept is the value of y when x is zero, which means where the graph intersects the y-axis. In this context, since the graph does not pass through the y-axis, there is no y-intercept. This implies that the value of y is not dependent solely on the value of x at zero.
d. The graph of the line represents the relationship between the x and y values based on the given data points. However, since the data points do not form a perfectly linear pattern, the exact relationship between x and y cannot be determined solely from these data points. The graph simply visually represents the general trend of increasing y-values as x-values increase.