I've to create a scatter plot using the following coordinates: (0,15.0), (1000,13.0), (2000,11.0), (3000,9.1) and (4000,7.1)
using these points i have to find a prediction equation. thus, i used the points (1000,13.0) and (3000,9.1) the equation i found was y = -0.00195x + 14.95. Am I doing right so far?
Well, I really do not get what precisely you're supposed to do. If you shall find a term of a function on whose graph the aforementioned points are located, you will have to make a LES (linear equation system).
y = ax^4+bx^3+cx^2+dx+e
Since 5 points are given, it is somewhat easy to either prove or deplore the existence of a unique solution. (Or that there doesn't even exist one at all...)
Well the x values represent the altitudes and the y values are the temperatures presented at each of the altitudes. Thus I've to find a prediction equation.
To create a scatter plot using the given coordinates, you can follow these steps:
1. On a graph paper or any graphing software, create a Cartesian coordinate system by labeling the x-axis and y-axis.
2. Plot the given points on the graph by locating the x-coordinate on the x-axis and the y-coordinate on the y-axis.
- Plot (0, 15.0) at the point (0, 15.0) on the graph.
- Plot (1000, 13.0) at the point (1000, 13.0).
- Plot (2000, 11.0) at the point (2000, 11.0).
- Plot (3000, 9.1) at the point (3000, 9.1).
- Plot (4000, 7.1) at the point (4000, 7.1).
3. Once all the points are plotted, connect them with straight lines. Since a scatter plot shows individual data points, you can mark the points with dots or small circles instead of connecting them.
Regarding the prediction equation you derived using the points (1000, 13.0) and (3000, 9.1), let's verify if it's correct:
1. Calculate the slope:
- Slope (m) = (change in y) / (change in x)
- Slope = (9.1 - 13.0) / (3000 - 1000) = -0.0039
2. Use the slope-intercept form (y = mx + b) to find the y-intercept (b):
- We can use either of the two given points to find 'b'.
- Using (1000, 13.0): 13.0 = -0.0039(1000) + b
=> 13.0 = -3.9 + b
=> b = 16.9
3. Now, form the final equation by substituting the slope (m) and y-intercept (b) into the slope-intercept form:
- y = -0.0039x + 16.9
Comparing this with your derived equation (y = -0.00195x + 14.95), it seems there was a calculation mistake. The correct equation is y = -0.0039x + 16.9, not y = -0.00195x + 14.95.