Accurately Determining Slope from Graphs: A Comprehensive Guide, Slides of Printing

Download Accurately Determining Slope from Graphs: A Comprehensive Guide and more Slides Printing in PDF only on Docsity! Finding slopes accurately. When calculating the slope of a line fitting the data, you must never use specific data points in the calculation. Instead, you should extend your line to the boundaries of your grid and use the two points where the line exits the grid. Using two widely separated points will allow a more precise estimate of the slope. Computer-generated graphs often have widely-spaced grid lines (if any at all) that make it difficult to read off these coordinates with much precision. When the printed grid lines are too widely spaced, you need to do a little more work to find the coordinates. This involves measuring distances on the graph with a ruler and finding the scale factors that relate distances to the units used in the measurement. This is illustrated in the following graph and discussion. An example is shown of data that seem to follow a straight line, Y = mX + b. After plotting the data and printing the graph, a straight line was drawn by hand to best represent the linear trend of the data. Finding the Y-intercept and the slope of the line is the usual analysis required. The line crosses the Y-axis at point A. The Y-coordinate of point A is the Y-intercept, b. To find the slope, m, we use the triangle formed by our best straight line connecting points A and B and the two horizontal and vertical lines shown: 𝑚 = Δ𝑌 Δ𝑋 = 𝑌! − 𝑌! 𝑋! − 𝑋!