Solving equations involving parallel and perpendicular lines examples
Solving equations involving parallel and perpendicular lines examples Solving equations involving parallel and perpendicular lines examples
Find an equation of the line that passes through each given point and is perpendicular to the line with the given equation. 19. (–2, 0); y = –3x + 7 m = –3 For a perpendicular line use m = 3 1 and (–2, 0) 0 = 3 1 (–2) + b b = 3 2 y = mx + b y = 3 1 x + 3 2 20. (2, 5); 3x + 5y = 7 3x + 5y = 7 y = m = 3 − 5 3 7 − x + 5 3 For a perpendicular line use m = 3 5 and (2, 5) 5 = 3 5 (2) + b b = 3 5 y = mx + b y = 3 5 x + 3 5 21. (0, –4); 6x – 3y = 5 6x – 3y = 5 y = 2x m = 2 5 − 3 For a perpendicular line use m = –4 = b = –4 1 − (0) + b 2 y = mx + b 1 y = − x – 4 2 1 − and (0, –4) 2 Solving Equations Involving Parallel and Perpendicular Lines www.BeaconLC.org©2001 September 22, 2001 12
22. (12, 6); 4 3 x + 2 1 y = 2 3 1 3 x + y = 2 y = − x + 4 4 2 2 3 m = − 2 2 For a perpendicular line use m = and (12, 6) 3 6 = 3 2 (12) + b b = –2 y = mx + b y = 3 2 x – 2 Find the value of “a” for which the graph of the first equation is perpendicular to the graph of the second equation. 23. y = ax – 5; 2y = 3x Rewrite 2y = 3x in slope-intercept form. y = 2 3 x Compare slopes with y = ax – 5. If a has a perpendicular slope then 2 3 (a) = –1 a = 2 − 3 24. y = ax + 2; 3y – 4x = 7 Rewrite 3y – 4x = 7 in slope-intercept form. y = 3 4 x + 3 7 Compare slopes with y = ax + 2. If a has a perpendicular slope then 3 4 (a) = –1 a = 3 − 4 Solving Equations Involving Parallel and Perpendicular Lines www.BeaconLC.org©2001 September 22, 2001 13
- Page 1 and 2: Solving Equations Involving Paralle
- Page 3 and 4: 7. Example - Find an equation of th
- Page 5 and 6: 13. Example - Find an equation of t
- Page 7 and 8: Name:___________________ Date:_____
- Page 9 and 10: Name:___________________ Date:_____
- Page 11: Find an equation of the line that p
- Page 15 and 16: Student Name: __________________ Da
22. (12, 6); 4<br />
3 x + 2<br />
1 y = 2<br />
3 1 3<br />
x + y = 2 y = − x + 4<br />
4 2 2<br />
3<br />
m = −<br />
2<br />
2<br />
For a <strong>perpendicular</strong> line use m = <strong>and</strong> (12, 6)<br />
3<br />
6 = 3<br />
2 (12) + b<br />
b = –2<br />
y = mx + b<br />
y = 3<br />
2 x – 2<br />
Find the value of “a” for which the graph of the first equation is <strong>perpendicular</strong> to<br />
the graph of the second equation.<br />
23. y = ax – 5; 2y = 3x<br />
Rewrite 2y = 3x in slope-intercept form.<br />
y = 2<br />
3 x Compare slopes with y = ax – 5.<br />
If a has a <strong>perpendicular</strong> slope then 2<br />
3 (a) = –1<br />
a =<br />
2<br />
−<br />
3<br />
24. y = ax + 2; 3y – 4x = 7<br />
Rewrite 3y – 4x = 7 in slope-intercept form.<br />
y = 3<br />
4 x + 3<br />
7<br />
Compare slopes with y = ax + 2.<br />
If a has a <strong>perpendicular</strong> slope then 3<br />
4 (a) = –1<br />
a =<br />
3<br />
−<br />
4<br />
<strong>Solving</strong> Equations Involving Parallel <strong>and</strong> Perpendicular Lines www.BeaconLC.org©2001 September 22, 2001<br />
13
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