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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Concept of Slope
Slope represents the rate of change between two points on a graph or in a table. It is calculated by finding the change in y-coordinates divided by the change in x-coordinates.
Step 3:: Identify the Slope Formula
- $$(x_{2}, y_{2})$$ is the second point
The slope formula is: Where:
Step 4:: Select Points from the Table
To find the slope, choose two points from the table. Ensure the points are different to avoid division by zero.
Step 5:: Calculate the Change in Y (Vertical Change)
\Delta y = y_{2} - y_{1}
Subtract the y-coordinates:
Step 6:: Calculate the Change in X (Horizontal Change)
\Delta x = x_{2} - x_{1}
Subtract the x-coordinates:
Step 7:: Divide the Changes
m = \frac{\Delta y}{\Delta x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}
Divide the change in y by the change in x:
Final Answer
To find the slope from a table, select two points, calculate the vertical and horizontal changes, then divide the change in y by the change in x using the slope formula m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}.
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