SECTION 1.5 Lines 43 Finding an Equation of a Line Perpendicular to a Given Line Find an equation of the line that contains the point ( ) − 1, 2 and is perpendicular to the line + = x y3 6. Graph the two lines. Solution EXAMPLE 12 First write the equation of the line + = x y3 6 in slope-intercept form to find its slope. + = = − + = − + x y y x y x 3 6 3 6 1 3 2 The slope of the line + = x y3 6 is − 1 3 .Any line perpendicular to this line has slope 3. Because the point ( ) − 1, 2 is on the line with slope 3, use the point-slope form of the equation of a line. ( ) ( ) ( ) ( ) − = − − − = − + = − y y m x x y x y x 2 3 1 2 3 1 1 1 To obtain other forms of the equation, proceed as follows: + = − = − − = y x y x x y 2 3 3 3 5 3 5 Figure 70 shows the graphs. Figure 70 x y 6 2 4 6 22 24 22 2 4 (1, 22) y 5 3x 2 5 x 1 3y 5 6 8 Y2 5 3x 2 5 28 25 5 Y1 5 2 x 1 2 1 3 Proceed to solve for y . Place in the form = + y mx b. Point-slope form = = =− m x y 3, 1, 2 1 1 Simplify. Slope-intercept form General form CAUTION Be sure to use a square screen when you graph perpendicular lines. Otherwise, the angle between the two lines will appear distorted. j Now Work PROBLEM 73 Concepts and Vocabulary 1.5 Assess Your Understanding 1. Interactive Figure Exercise Exploring Slope Open the “Slope” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Sullivan Interactive Figures). (a) Be sure the “Show Slope” box is not checked. Grab point B and move it to the point with coordinates ( ) 3, 5 . What is the value of the “Rise”? What is the value of the “Run”? Select the “Show Slope” box. What is the value of the slope? (b) Grab point B and move it to the point with coordinates ( ) − 4, 3 . What is the value of the slope? (c) What is the value of the slope if the line is horizontal? (d) Multiple Choice Which of the following lines have a slope that is negative? Select all that apply. (i) The line through ( ) 1, 3 and ( ) 4, 4 (ii) The line through ( ) 1, 3 and ( ) 4, 2 (iii) The line through ( ) 1, 3 and ( ) 1, 6 (iv) The line through ( ) 1, 3 and ( ) −1, 5 (v) The line through ( ) 1, 3 and ( ) −1, 0 (e) Multiple Choice If the value of the “run” is positive and remains unchanged, then as the value of the “rise” decreases, the slope of the line . (i) Increases (ii) Decreases (iii) Remains unchanged (iv) Cannot be determined 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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