Warm Up x – 5 = 0 Write the Standard Form equation of the line that passes through the points (5, 2) and (5, –3). m = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 = −3 −2 5 −5 x = 5 = −5 0 x – 5 = 0 undefined
Parallel & Perpendicular Lines Parallel Lines - coplanar lines that do not intersect - have the same slope and different y-intercepts Perpendicular Lines - intersect to form 4 right angles - slopes are the opposite sign and reciprocal of one another
1. y = 3x – 2 2. y = 8x – 1 x + 3y = –9 7x – y – 1 = 0 3y = –x – 9 Find the slope of each line. Then determine whether the lines are parallel, perpendicular, or neither… 1. y = 3x – 2 2. y = 8x – 1 x + 3y = –9 7x – y – 1 = 0 3y = –x – 9 –y = –7x + 1 y = – 1 3 x – 3 y = 7x – 1 m = – 1 3 m = 3 m = 8 m = 7 Perpendicular Lines Neither
3. y = x – 9 4. y = 2x + 4 x – y + 9 = 0 x + 2y + 10 = 0 2y = –x – 10 Find the slope of each line. Then determine whether the lines are parallel, perpendicular, or neither… 3. y = x – 9 4. y = 2x + 4 x – y + 9 = 0 x + 2y + 10 = 0 2y = –x – 10 –y = –x – 9 y = x + 9 y = − 1 2 x – 5 m = – 1 2 m = 1 m = 1 m = 2 Parallel Lines Perpendicular Lines
4x – y + 3 = 0 –y = –4x – 3 m = 4, (2, –3) y – 𝑦 1 = m(x – 𝑥 1 ) 5. Write the standard form equation of the line that passes through (2, –3) and is parallel to the line… 4x – y + 3 = 0 –y = –4x – 3 m = 4, (2, –3) y – 𝑦 1 = m(x – 𝑥 1 ) y = 4x + 3 y – (–3) = 4(x – 2) m = 4 y + 3 = 4(x – 2) 4x – y – 11 = 0 y + 3 = 4x – 8
3x + 2y + 1 = 0 m = – 3 2 , (3, –5) –3y = –2x – 6 y = 2 3 x + 2 6. Write the standard form equation of the line that passes through (3, –5) and is perpendicular to the line… 2x – 3y + 6 = 0 –3y = –2x – 6 m = – 3 2 , (3, –5) y = 2 3 x + 2 y – 𝑦 1 = m(x – 𝑥 1 ) y – (–5) = – 3 2 (x – 3) m = 2 3 y + 5 = – 3 2 (x – 3) 2y + 10 = –3x + 9 y + 5 = – 3 2 x + 9 2 3x + 2y + 1 = 0
7. a. Write the standard form equation of the line that passes through (2, 3) and is parallel to the line… y – 5 = 0 b. What is the equation of the line that is perpendicular ? y = 3 m = 0 m = 0 y – 3 = 0 x = 2 m = 0 m = undefined x – 2 = 0
8. a. Write the standard form equation of the line that passes through (–1, 4) and is parallel to the line… x + 3 = 0 b. What is the equation of the line that is perpendicular ? x = –1 m = undefined x + 1 = 0 m = undefined y = 4 m = undefined y – 4 = 0 m = 0
9. For what value of k is the graph of kx – 7y + 10 = 0 parallel to the graph of 8x – 14y + 3 = 0? For what value of k are the graphs perpendicular? parallel kx – 7y + 10 = 0 8x – 14y + 3 = 0 𝑘 7 = 4 7 –7y = –kx – 10 –14y = –8x – 3 y = 𝑘 7 x + 10 7 k = 4 y = 8 14 x + 3 14 perpendicular m = 𝑘 7 y = 4 7 x + 3 14 4k = –49 𝑘 7 = – 7 4 k = − 49 4 m = 4 7
10. For what value of k is the graph of 2x – ky + 5 = 0 parallel to the graph of 3x + 7y + 15 = 0? For what value of k are the graphs perpendicular? parallel 2x – ky + 5 = 0 3x + 7y + 15 = 0 2 𝑘 = – 3 7 –3k = 14 –ky = –2x – 5 7y = –3x – 15 y = 2 𝑘 x + 5 𝑘 k = – 14 3 y = – 3 7 x – 15 7 m = 2 𝑘 perpendicular m = – 3 7 7k = 6 2 𝑘 = 7 3 k = 6 7