How to Determine the Equation of a Line

How to Determine the Equation of a Line There are many instances in science and math in which you will need to determine the equation of a line. In chemistry, youll use linear equations in gas calculations, when analyzing rates of reaction, and when performing Beers 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 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 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 x0 in the equation of the line. The y-intercept is at the point (0, 34/5).