Finding the greatest slope on a graph involves identifying the steepest incline between two points on the graph. The slope is calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).
To find the greatest slope, follow these steps:
- Select two points: Choose pairs of points on the graph that you suspect might have the steepest slope.
- Calculate the slope: Use the slope formula, which is:
- Compare slopes: Repeat this for multiple pairs of points. The pair that gives you the largest absolute value of slope represents the greatest slope on the graph.
slope (m) = (y2 - y1) / (x2 - x1)It’s important to note that if the graph is a straight line, the slope will be constant. If it’s curved, the greatest slope might change depending on the section of the graph you are examining. In such a case, you may want to use calculus to find the derivative of the function, which will give you the slope at any point, allowing you to determine the maximum slope across the entire graph.