1. GEOMETRY HELP Find and compare the slopes of the lines. Each line has slope –1. The y-intercepts are 3 and –7. The lines have the same slope and different y-intercepts, so they are parallel. Slope of line 1 = = = = –1 y 2 – y 1 x 2 – x 1 5 – 3 –2 – 0 2 –2 Slope of line 2 = = = = –1 y 2 – y 1 x 2 – x 1 –10 –(–7) 3 – 0 –3 3 Quick Check Slopes of Parallel and Perpendicular Lines LESSON 3-7 Additional Examples Line 1 contains P(0, 3) and Q(–2, 5). Line 2 contains R(0, –7) and S(3, –10). Are lines 1 and 2 parallel? Explain.

2. GEOMETRY HELP Are the lines y = –5x + 4 and x = –5y + 4 parallel? Explain. The equation y = –5x + 4 is in slope-intercept form. Write the equation x = –5y + 4 in slope-intercept form. The line y = –5x + 4 has slope –5. The lines are not parallel because their slopes are not equal. x = –5y + 4 x – 4 = –5ySubtract 4 from each side. – x + = yDivide each side by –5. y = – x + 1515 4545 1515 4545 The line x = –5y + 4 has slope –. 1515 Slopes of Parallel and Perpendicular Lines LESSON 3-7 Additional Examples Quick Check

3. GEOMETRY HELP Write an equation in point-slope form for the line parallel to 6x – 3y = 9 that contains (–5, –8). Step 1: To find the slope of the line, rewrite the equation in slope-intercept form. 6x – 3y = 9 –3y = –6x + 9 Subtract 6x from each side. y = 2x – 3 Divide each side by –3. The line 6x – 3y = 9 has slope 2. Step 2: Use point-slope form to write an equation for the new line. y – y 1 = m(x – x 1 ) y – (–8) = 2(x – (–5)) Substitute 2 for m and (–5, –8) for (x 1, y 1 ). y + 8 = 2(x + 5) Simplify. Slopes of Parallel and Perpendicular Lines LESSON 3-7 Additional Examples Quick Check

4. GEOMETRY HELP Step 2: Find the product of the slopes. m 1 m 2 = – – = 1 2727 7272 Line 1 contains M(0, 8) and N(4, –6). Line 2 contains P(–2, 9) and Q(5, 7). Are lines 1 and 2 perpendicular? Explain. m 1 = slope of line 1 = = = = – y 2 – y 1 x 2 – x 1 –6 – 8 4 – 0 –14 4 7272 m 2 = slope of line 2 = = = = – y 2 – y 1 x 2 – x 1 7 – 9 5 – (–2) –2 7 2727 Lines 1 and 2 are not perpendicular because the product of their slopes is not –1. Step 1: Find the slope of each line. Slopes of Parallel and Perpendicular Lines LESSON 3-7 Additional Examples Quick Check

5. GEOMETRY HELP Write an equation for a line perpendicular to 5x + 2y = 1 that contains (10, 0). Step 1: To find the slope of the given line, rewrite the equation in slope-intercept form. 5x + 2y = 1 2y = –5x + 1 Subtract 5x from each side. y = – x + Divide each side by 2. 5252 1212 The line 5x + 2y = 1 has slope –. 5252 Step 2: Find the slope of a line perpendicular to 5x + 2y = 1. Let m be the slope of the perpendicular line. – m = –1 The product of the slopes of perpendicular lines is –1. m = –1 ( – ) Multiply each side by –. m = Simplify. 5252 2525 2525 2525 Slopes of Parallel and Perpendicular Lines LESSON 3-7 Additional Examples

6. GEOMETRY HELP Step 3: Use point-slope form, y – y 1 = m(x – x 1 ), to write an equation for the new line. (continued) 2525 y = (x – 10) Simplify. Slopes of Parallel and Perpendicular Lines LESSON 3-7 Additional Examples Quick Check y – 0 = (x – 10) Substitute for m and (10, 0) for (x 1, y 1 ). 2525 2 5

7. GEOMETRY HELP The equation for a line containing a lead strip is y = x – 9. Write an equation for a line perpendicular to it that contains (1, 7). 1212 Step 1: Identify the slope of the given line. slope y = x – 9 1212 Step 2: Find the slope of the line perpendicular to the given line. Let m be the slope of the perpendicular line. m = –1The product of the slopes of perpendicular lines is –1. m = –2Multiply each side by 2. 1212 Slopes of Parallel and Perpendicular Lines LESSON 3-7 Additional Examples

8. GEOMETRY HELP y – y 1 = m(x – x 1 ) y – 7 = –2(x – 1)Substitute –2 for m and (1, 7) for (x 1, y 1 ). (continued) Step 3: Use point-slope form to write an equation for the new line. Step 4: Write the equation in slope-intercept form. y – 7 = –2(x – 1) y – 7 = –2x + 2Use the Distributive Property. y = –2x + 9Add 7 to each side. Slopes of Parallel and Perpendicular Lines LESSON 3-7 Additional Examples Quick Check