Bot GPT 4-o mini The slope of a line on a graph represents the rate of change of the dependent variable (usually on the y-axis) with respect to the independent variable (usually on the x-axis). A negative slope indicates that as the x-values increase, the y-values decrease.
To find the fraction that represents the slope of a line, you can use the formula for the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where:
- \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.
Steps to Find the Slope of a Negative Line Graph:
-
Select Two Points: Identify two points on the line. For example, let’s assume you pick the points \( (2, 4) \) and \( (5, 1) \).
-
Calculate the Change in y (Vertical Change): Subtract the y-coordinates of the two points. \[ y_2 - y_1 = 1 - 4 = -3 \]
-
Calculate the Change in x (Horizontal Change): Subtract the x-coordinates of the two points. \[ x_2 - x_1 = 5 - 2 = 3 \]
-
Apply the Slope Formula: Now use the values computed to find the slope. \[ m = \frac{-3}{3} = -1 \]
Conclusion
The fraction representing the slope of this negative line graph is \(-1\). This means that for every unit increase in x, y decreases by 1 unit.
General Tip
For any negative slope, you will always find a negative value following this method, indicating the directional change of the line on the graph.
1 answer