Science, Tech, Math › Science How to Determine the Equation of a Line Share Flipboard Email Print Josef F. Stuefer / Getty Images Science Chemistry Basics Chemical Laws Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry In Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate By Anne Marie Helmenstine, Ph.D. Chemistry Expert Ph.D., Biomedical Sciences, University of Tennessee at Knoxville B.A., Physics and Mathematics, Hastings College Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. She has taught science courses at the high school, college, and graduate levels. our editorial process Facebook Facebook Twitter Twitter Anne Marie Helmenstine, Ph.D. Updated July 22, 2018 There are many instances in science and math in which you will need to determine the equation of a line. In chemistry, you'll use linear equations in gas calculations, when analyzing rates of reaction, and when performing Beer's Law calculations. Here are a quick overview and example of how to determine the equation of a line from (x,y) data. There are different forms of the equation of a line, including the standard form, point-slope form, and slope-line intercept form. If you are asked to find the equation of a line and are not told which form to use, the point-slope or slope-intercept forms are both acceptable options. Standard Form of the Equation of a Line One of the most common ways to write the equation of a line is: Ax + By = C where A, B, and C are real numbers Slope-Intercept Form of the Equation of a Line A linear equation or equation of a line has the following form: y = mx + b m: slope of the line; m = Δx/Δy b: y-intercept, which is where the line crosses the y-axis; b = yi - mxi The y-intercept is written as the point (0,b). Determine the Equation of a Line - Slope-Intercept Example Determine the equation of a line using the following (x,y) data. (-2,-2), (-1,1), (0,4), (1,7), (2,10), (3,13) First calculate the slope m, which is the change in y divided by the change in x: y = Δy/Δx y = [13 - (-2)]/[3 - (-2)] y = 15/5 y = 3 Next calculate the y-intercept: b = yi - mxi b = (-2) - 3*(-2) b = -2 + 6 b = 4 The equation of the line is y = mx + b y = 3x + 4 Point-Slope Form of the Equation of a Line In the point-slope form, the equation of a line has slope m and passes through the point (x1, y1). The equation is given using: y - y1 = m(x - x1) where m is the slope of the line and (x1, y1) is the given point Determine the Equation of a Line - Point-Slope Example Find the equation of a line passing through points (-3, 5) and (2, 8). First determine the slope of the line. Use the formula: m = (y2 - y1) / (x2 - x1)m = (8 - 5) / (2 - (-3))m = (8 - 5) / (2 + 3)m = 3/5 Next use the point-slope formula. Do this by choosing one of the points, (x1, y1) and putting this point and the slope into the formula. y - y1 = m (x - x1)y - 5 = 3/5 (x - (-3))y - 5 = 3/5 (x + 3)y - 5 = (3/5)(x + 3) Now you have the equation in point-slope form. You could proceed to write the equation in slope-intercept form if you wish to see the y-intercept. y - 5 = (3/5)(x + 3)y - 5 = (3/5)x + 9/5y = (3/5)x + 9/5 + 5y = (3/5)x + 9/5 + 25/5y = (3/5)x +34/5 Find the y-intercept by setting x=0 in the equation of the line. The y-intercept is at the point (0, 34/5).