Find the slope of a graph

Learning Objectives Define slope as the ratio of vertical change to horizontal change. Visually identify whether the slope of a line is positive, negative, zero, or undefined. Calculate the slope of a line from a graph by counting the 'rise' and 'run'. Determine the coordinates of two points on a line and use the slope formula to calculate the slope. Explain the relationship between the steepness of a line and the absolute value of its slope. Interpret the slope as a rate of change in a real-world context represented by a graph. Ever wondered how engineers design a roller coaster's thrilling drops or a safe wheelchair ramp? 🎢 It all comes down to understanding steepness! In this tutorial, you will learn how to measure the steepness of a line on a g...

TermDefinitionExample SlopeA number that measures the steepness and direction of a line. It is the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on the line.A slope of 2 means that for every 1 unit you move to the right on the graph, you must move 2 units up. RiseThe vertical change between two points on a line. It can be positive (up) or negative (down).If you move from the point (1, 2) to (3, 7), the rise is 7 - 2 = 5. RunThe horizontal change between two points on a line. It can be positive (right) or negative (left).If you move from the point (1, 2) to (3, 7), the run is 3 - 1 = 2. Positive SlopeA line that goes upward from left to right. This indicates a positive rate of change.A graph showing the distance you travel over time as yo...

Rise Over Run Formula m = \frac{\text{rise}}{\text{run}} Use this when you can easily count the vertical and horizontal units between two points directly on the graph. It's a visual method. Slope Formula m = \frac{y_2 - y_1}{x_2 - x_1} Use this when you have the coordinates of any two points on the line, (x₁, y₁) and (x₂, y₂). This is the most reliable algebraic method.