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2.9A Parallel and Perpendicular Lines Warm Up Solve each equation for y. 1. y – 6x = 9 2. 4x – 2y = 8 2.9A Parallel and Perpendicular Lines Objectives Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding. Pairs of Lines Parallel Lines Perpendicular Lines Intersecting Lines Same slope & Slopes are opposite Different slopes Relationship different y-intercept reciprocals Example 𝑦 = 𝟓𝑥 + 8 𝑦 = 𝟓𝑥 − 4 𝟑 𝑦 = 𝑥−7 𝟒 𝟒 𝑦 =− 𝑥+2 𝟑 𝑦 = 𝟑𝑥 − 6 𝑦 = 𝟐𝑥 − 9 Decide whether the lines are parallel, perpendicular, or neither. ** You will sometimes need to first: solve the equations for y, and then: identify the slopes to answer the problem. Example 1: y = 3x + 7 y = –3x – 4 Example 2: 𝑥 + 3𝑦 = 5 6𝑦 = −2𝑥 + 12 Example 3: 2y – 4x = 16 y – 10 = 2(x - 1) Example 4: 3x + 5y = 2 3x + 6 = -5y Example 5: 2y = 4x + 12 4x – 2y = 8 State what the slope would be for a parallel line and for a perpendicular line to the given line. ** You may need to first solve the equation for y in order to identify the slope. Example 6: 3x + 5y = 2 Example 7: y – 5 = 2(x + 3) Example 8: 3x + 6 = -5y Example 9: Find the slope and the y-intercept of each line to write the equation of the line in slope-intercept form.