Final answer:
Calculating slope from a table or from points on a graph involves similar steps, such as selecting two points, finding the differences in x and y-coordinates, and dividing the rise by the run. It's recommended to use points that are widely separated to reduce error.
Step-by-step explanation:
Finding the slope from a table of data and finding the slope from two points on a graph involve similar processes. The fundamental concept of slope, defined as the ratio of the change in the y-coordinate to the change in the x-coordinate (rise over run), applies in both scenarios. Whether you are deriving the slope from a table or calculating it between two points on a graph, the steps you take will be essentially the same:
- Select two distinct points. In the context of a table, these would be two different rows of data, and on the graph, they would be two points along the line.
- Determine the differences in the y-coordinates (rise) and x-coordinates (run) between these two points.
- Divide the difference in y-coordinates by the difference in x-coordinates to obtain the slope.
It's important to choose points that are farther apart to minimize potential errors, whether reading from a graph or interpreting table data. The consistency of the slope for a linear relationship allows any two points to be used for its determination.