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messersmith_power_intermediate_algebra_1e_ch4_7_10

EXAMPLE 7 Find the standard form for the equation of the line that contains the point (5, 3) and is perpendicular to 5x 2y 6. Solution Begin by fi nding the slope of 5x 2y 6 by putting it into slope-intercept form. 5x 2y 6 2y 5x 6 Add 5x to each side. y 5 2 x 6 2 Divide by 2. y 5 2 x 3 Simplify. m 5 2 Then, determine the slope of the line containing (5, 3) by fi nding the negative reciprocal of the slope of the given line. mperpendicular 2 5 The line for which we need to write an equation has m 2 5 and contains the point (5, 3). Use the point-slope formula to fi nd an equation of the line. Substitute 2 5 for m. Substitute (5, 3) for (x1, y1). y y1 m(x x1) y 3 2 5 x (5) Substitute 5 for x1 and 3 for y1. y 3 2 5 (x 5) y 3 2 5 x 2 Distribute. Since we are asked to write the equation in standard form, eliminate the fraction by multiplying each side by 5. 5( y 3) 5 a 2 5 x 2b 5y 15 2x 10 Distribute. 5y 2x 5 Add 15 to each side. 2x 5y 5 Add 2x to each side. The equation is 2x 5y 5. Write down the steps as you are reading the example. YOU TRY 7 Find the equation of the line perpendicular to 3x y 2 containing the point (9, 4). Write the equation in standard form. www.mhhe.com/messersmith SECTION 4.3 Writing an Equation of a Line 179


messersmith_power_intermediate_algebra_1e_ch4_7_10
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