Explain how to find the slope of a line from a table of data.
To find the slope of a line from a table of data, you need to remember that slope is defined as the change in the y-coordinate divided by the change in the x-coordinate. Here's a step-by-step process:
1. Start by examining your table of data, which should contain pairs of x and y values.
2. Identify two points on the line from the table of data. Let's call them Point 1 and Point 2. Make sure these points are not at the same x-coordinate since the slope is undefined in such cases.
3. Determine the x and y coordinates of both points. For example, Point 1 may have coordinates (x1, y1), and Point 2 may have coordinates (x2, y2).
4. Calculate the change in y-coordinates by subtracting the y-coordinate of Point 1 from the y-coordinate of Point 2. This can be represented as Δy = y2 - y1.
5. Calculate the change in x-coordinates by subtracting the x-coordinate of Point 1 from the x-coordinate of Point 2. This can be represented as Δx = x2 - x1.
6. Use the formula for slope: slope = Δy / Δx. Divide the change in y-coordinates (Δy) by the change in x-coordinates (Δx) to obtain the slope of the line.
7. Simplify the result if necessary, and you now have the slope of the line from the table of data.
By following these steps, you can determine the slope of a line from a table of data.