3 Use the Point-Slope Formula to Write an Equation of a Line Given Two Points on the Line We are now ready to discuss how to write an equation of a line when we are given two points on a line. Procedure Write an Equation of a Line Given Two Points on the Line To write an equation of a line given two points on the line, a) use the points to fi nd the slope of line then b) use the slope and either one of the points in the point-slope formula. EXAMPLE 3 Write an equation of the line containing the points (6, 4) and (3, 2). Express the answer in slope-intercept form. Solution We are given two points on the line, so fi rst we will fi nd the slope. m 2 4 3 6 2 3 2 3 We will use the slope and either one of the points in the point-slope formula. (Each point will give the same result.) We will use (6, 4). Substitute 2 3 for m. Substitute (6, 4) for (x1, y1). y y1 m(x x1) y 4 2 3 (x 6) Substitute 6 for x1 and 4 for y1. y 4 2 3 x 4 Distribute. y 2 3 x Add 4 to each side to solve for y. The slope-intercept form of the equation is y 2 3 x. In this example, substitute (3, 2) for (x, y) and verify that you get the same result. YOU TRY 3 Find the standard form for the equation of the line containing the points (2, 5) and (1, 1). 174 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
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