1. NOTES Parallel Lines and Word Problems

2. Parallel Lines Lines that never Lines that never intersect intersect We can tell two lines We can tell two lines are parallel if we graph are parallel if we graph them OR them OR If we look at their slope If we look at their slope What do we notice about What do we notice about the slope of the lines on the the slope of the lines on theleft? y x 5 5 -5 Slopes are the same!

3. Example #1 Decide whether the graphs of the two equations are parallel lines. Explain your reasoning. line a: -x + 2y = 6line b: -x + 2y = -2 line a: -x + 2y = 6line b: -x + 2y = -2 Which means? Look to see if they have same slope. Step 1: rewrite equations in y = mx + b Step 2: compare the slopes TRY ON YOUR OWN

4. Example #1 cont. Decide whether the graphs of the two equations are parallel lines. Explain your reasoning. line a: -x + 2y = 6 line b: -x + 2y = -2 line a: -x + 2y = 6 line b: -x + 2y = -2 +x +x +x +x +x +x +x +x 2y = x+6 2y = x - 2 2y = x+6 2y = x - 2 2 2 2 2 2 2 2 2 2 2 2 2 Line a: y = ½x + 3 Line b: y = ½x – 1 Yes, lines are parallel since they have the same slope.

5. Example #2 Decide whether the graphs of the two equations are parallel lines. Explain your reasoning. line a: 3y = -9x – 5 line b: 2y – 6x = -5 TRY ON YOUR OWN

6. Example #2 cont. Decide whether the graphs of the two equations are parallel lines. Explain your reasoning. line a: 3y = -9x – 5 line b: 2y – 6x = -5 line a: m = -3 line b: m = 3 NO, lines are not parallel. The slope of the lines are different.

7. Example #3 A submarine started to decrease from a depth of 5 feet below the water at a rate of ½ feet per hour. The equation y = –½ x – 5 models the depth y of the submarine after x hours.

8. Example #3 A submarine started to decrease from a depth of 5 feet below the water at a rate of ½ feet per hour. The equation y = – ½ x – 5 models the depth y of the submarine after x hours. A submarine started to decrease from a depth of 5 feet below the water at a rate of ½ feet per hour. The equation y = – ½ x – 5 models the depth y of the submarine after x hours. a) What is the slope of y = –½ x – 5 ? What is the y- intercept? Slope = m = -½ y-intercept = - 5

9. Example #3 A submarine started to decrease from a depth of 5 feet below the water at a rate of ½ feet per hour. The equation y = -½ x – 5 models the depth y of the submarine after x hours. A submarine started to decrease from a depth of 5 feet below the water at a rate of ½ feet per hour. The equation y = -½ x – 5 models the depth y of the submarine after x hours. b) Explain what the slope and y-intercept mean in relation to the problem. Slope is the rate at which the submarine is going down. Slope is the rate at which the submarine is going down. The y-intercept is the depth of the submarine at the very beginning The y-intercept is the depth of the submarine at the very beginning

10. Example #3 C) Graph the depth of the Submarine over a 6 hour period of time

11. Example #3 A submarine started to decrease from a depth of 5 feet below the water at a rate of ½ feet per hour. The equation y = –½ x – 5 models the depth y of the submarine after x hours. A submarine started to decrease from a depth of 5 feet below the water at a rate of ½ feet per hour. The equation y = –½ x – 5 models the depth y of the submarine after x hours. d)If the submarine gets a depth of 12 feet, it will need repairing. Is it going to get down to 12 feet in 6 hours? Look at your graph…. No, after 6 hours the submarine will only be at a depth of 8 feet below the water