Find the slope from a table - Algebra-1

1. Fundamental Concepts

Definition: The slope of a line is a measure of its steepness and is calculated as the change in y divided by the change in x (rise over run).
Formula: Slope $ m = \frac{{\Delta y}}{{\Delta x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}} $
Interpretation: A positive slope indicates an upward trend, while a negative slope indicates a downward trend.

Basic Rule: $$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$$

Consistency: The slope remains constant for a straight line regardless of which two points are chosen.

Application: Used to analyze trends in data sets and predict future values.

Problem: Find the slope from the following table:

Select two points from the table, e.g., (1, 3) and (3, 7).
Calculate the change in y and x: $\Delta y = 7 - 3 = 4$ and $\Delta x = 3 - 1 = 2$.
Compute the slope: $m = \frac{{4}}{{2}} = 2$.

Validation: Check consistency with another pair of points, e.g., (2, 5) and (3, 7): $m = \frac{{7 - 5}}{{3 - 2}} = 2$. ✓

Problem: Find the slope from the following table:

Select two points from the table, e.g., (-2, 4) and (2, 0).
Calculate the change in y and x: $\Delta y = 0 - 4 = -4$ and $\Delta x = 2 - (-2) = 4$.
Compute the slope: $m = \frac{{-4}}{{4}} = -1$.

Validation: Check consistency with another pair of points, e.g., (0, 2) and (2, 0): $m = \frac{{0 - 2}}{{2 - 0}} = -1$. ✓

Visual Strategy: Plot the points on a coordinate plane to visualize the slope.
Error-Proofing: Always double-check calculations by using different pairs of points from the table.
Concept Reinforcement: Practice finding slopes from various tables to reinforce understanding.