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U1B L1 Review of Slope UNIT 1B LESSON 1 Review of Slope

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U1B L1 Review of Slope Slope of a Line The term slope is often used to describe steepness or rate of change. The pitch of a roof, the steepness of a ski run, the speed of a car are all examples of slope. In each case, the slope is the ratio of the rise to the run In a coordinate system, we can determine the slope of any line segment from its endpoints P1(x1, y1) and P2(x2, y2). From P1 to P2: the rise is the difference in the y-coordinates: y2 – y1 or ∆y the run is the difference in the x-coordinates: x2 – x1 or ∆x

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U1B L1 Review of Slope Slope of a Line

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U1B L1 Review of Slope Slope of a Line A line that goes uphill as x increases has a positive slope.. A line that goes downhill as x increases has a negative slope.

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U1B L1 Review of Slope Slope of a Line A horizontal line has slope zero since all of its points have the same y-coordinate. P1(-1, 1) P2(2, 1) 𝒎= 𝟏−𝟏 𝟐−(−𝟏) = 𝟎 𝟑 =𝟎 For vertical lines, the slope is undefined since all of its points have the same x-coordinate P1 (1.5, 2) P2 (1.5, -1) 𝒎= 𝟐 −(−𝟏) 𝟏.𝟓−𝟏.𝟓 = 𝟑 𝟎 division by 0 is undefined

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**Parallel Lines Parallel lines form equal angles with the x-axis.**

U1B L1 Review of Slope Parallel Lines Parallel lines form equal angles with the x-axis. Hence, non-vertical parallel lines have the same slope. m1 = m2

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U1B L1 Review of Slope Perpendicular Lines If two non-vertical lines L1 and L2 are perpendicular, their slopes m1 and m2 satisfy m1m2 = – 1, so each slope is the negative reciprocal of the other: Line 1 Slope = 𝟑 𝟏 =𝟑 3 1 ×− 1 3 =−1 Line 2 Slope = − 𝟏 𝟑

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**Lines that have equal slopes are parallel**

UNIT 1B L1 REVIEW OF SLOPE PAGE 1 A(2, 1), B(5, 3) 𝒎= 𝟏−𝟑 𝟐−𝟓 = −𝟐 −𝟑 = 𝟐 𝟑 Run = 3 Run = 3 Rise = 2 C(– 2, 2), D(1, 4) Rise = 2 𝒎= 𝟐−𝟒 −𝟐−𝟏 = −𝟐 −𝟑 = 𝟐 𝟑 Lines that are higher on the right have a positive slope. Lines that have equal slopes are parallel AB // CD and EF // GH

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**Lines that have equal slopes are parallel**

E(– 3 , 4), F(– 1 , – 2) 𝒎= 𝟒−(−𝟐) −𝟑−(−𝟏) = 𝟔 −𝟐 =−𝟑 Run = – 1 Rise = 3 G(0, 5), H(1, 2) Rise = – 6 𝒎= 𝟓−𝟐 𝟎−𝟏 = 𝟑 −𝟏 =−𝟑 Run = 2 Lines that are higher on the left have a negative slope. Lines that have equal slopes are parallel AB // CD and EF // GH

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**If the slopes of 2 lines are negative reciprocals **

J(3 , –2), K(6 , – 4) 𝒎= −𝟐−(−𝟒) 𝟑−𝟔 = 𝟐 −𝟑 =− 𝟐 𝟑 L(4, –3), M(2, –6) Run = –3 𝒎= −𝟑−(−𝟔) 𝟒−𝟐 = 𝟑 𝟐 Run = 2 Rise = 2 Rise = 3 − 𝟐 𝟑 × 𝟑 𝟐 =−𝟏 If the slopes of 2 lines are negative reciprocals (product = – 1) they are perpendicular. JK ┴ LM

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**They are also perpendicular**

R(– 2 , 4), S(5 , 4) 𝒎= 𝟒−𝟒 −𝟐−𝟓 = 𝟎 −𝟕 =𝟎 P(– 3, – 2 ), Q(– 3, 3) 𝒎= −𝟐−𝟑 −𝟑−(−𝟑) = −𝟔 𝟎 ÷ by 0 is undefined Horizontal lines will always have a slope of zero Vertical lines will always have a slope which is undefined. They are also perpendicular

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**What is the slope of the line and what does it represent?**

U1B L1 Review of Slope QUESTION 9: Two students entered a car rally. During part of the rally, they had to drive at a constant speed. The following graph shows the distance traveled over a given time while traveling at this constant speed. Distance (km) Time (hours) What is the slope of the line and what does it represent? P2 P1 Slope = (180 km – 60 km) = 60 km/h (3 h – 1 h) It represents the velocity of the car.

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U1B L1 Review of Slope QUESTION 10 The pool at a fitness club is being drained. The graph shows the number of kilolitres of water remaining after an elapsed time. b) What is the intercept along the vertical axis and what does this intercept represent? c) What is the intercept along the horizontal axis and what does this intercept represent? a) What is the slope of the line and what does it represent? The horizontal intercept is (400, 0) The vertical intercept is (0, 100) It takes 400 min to drain the pool. Slope = (40 kL – 100kL) (240 min – 0 min) = – 0.25kL/min The pool has 100 kL in it before it is drained. The pool is draining at a rate of 0.25 kL/min

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