Formula Point-Slope Formula The point-slope form of a line is y y1 m(x x1), where (x1, y1) is a point on the line and m is its slope. Procedure Write an Equation of a Line Given Its Slope and a Point on the Line If we are given the slope of the line and a point on the line, we can use the point-slope formula to fi nd an equation of the line. Note The point-slope formula will help us write an equation of a line. We will not express our final answer in this form. We will write our answer in either slope-intercept form or in standard form. EXAMPLE 2 A line has slope 3 and contains the point (2, 1). Find the standard form for the equation of the line. Solution Although we are told to fi nd the standard form for the equation of the line, we do not try to immediately “jump” to standard form. First, ask yourself, “What information am I given?” We are given the slope and a point on the line. Therefore, we will begin by using the point-slope formula. Our last step will be to put it in standard form. Use y y1 m(x x1). Substitute 3 for m. Substitute (2, 1) for (x1, y1). y y1 m(x x1) y 1 3(x 2) Substitute 2 for x1 and 1 for y1. y 1 3x 6 Distribute. Since we are asked to express the answer in standard form, we must get the x- and y-terms on the same side of the equation. 3x y 1 6 Add 3x to each side. 3x y 7 Add 1 to each side. In standard form, the equation is 3x y 7. Notice that the ordered pair (2, 1) is not the y-intercept because the x-value is not 0. Therefore you are not given b so we will not use y mx b in this example. YOU TRY 2 A line has slope 5 and contains the point (1, 3). Find the standard form for the equation of the line. www.mhhe.com/messersmith SECTION 4.3 Writing an Equation of a Line 173
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