LU 3 System of Equations and Functions_answer.pptx - LU3 System of Equation Functions Coordinate of point Slope gradient of line Equation of straight

LU 3 System of Equations and Functions_answer.pptx - LU3...

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LU3 System of Equation & Functions Coordinate of point Slope / gradient of line Equation of straight line System of Equation Functions Graphs of Functions Operations with Functions Composite Functions 1
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If A(-3,4) & B(1,2) i) Find the distance between the points ii) Find the mid-point of AB Example 1 2
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If A(-3,4) & B(1,2) i) Find the distance between the points ii) Find the mid-point of AB Solution – Example 1 3 47 . 4 5 2 ) 5 )( 4 ( 20 4 16 ) 2 4 ( 1 3 2 2 2 2 1 2 2 1 y y x x 3 , 1 2 6 , 2 2 2 2 4 , 2 1 3 2 , 2 2 1 2 1 y y x x
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Identify the gradient and the y-intercept of the following:- 4 x y c x y b x y a 8 1 2 ) ( 5 3 1 ) ( 3 ) (
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Find the gradient of the following coordinates:- Example 2 a)A (1,3) & B (2,1) b)A (-2,5) & B (-6,-1) c) Find the slope m of the line that goes through the points (–2, 5) and (3, 5) . 5
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Find the gradient of the following coordinates:- (a) A(1,3) & B(2,1) (b) A(-2,5) & B(-6,-1) Solution - Example 2 6 2 1 2 3 1 1 2 1 2 m m x x y y m 2 3 4 6 2 6 5 1 1 2 1 2 m m m x x y y m
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–2 –1 1 2 3 4 Solution-Example 2c Find the slope m of the line that goes through the points (–2, 5) and (3, 5) . x 1 = –2 , y 1 = 5 , x 2 = 3 , y 2 = 5; The slope of a horizontal line is zero : y x L 6 4 3 2 1 (–2, 5) (3, 5) m = 0 7 2 1 2 1 5 5 0 0 3 ( 2) 5 y y m x x
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EXAMPLE 3 Determine whether the following lines are parallel or perpendicular:- 8 3 6 4 & 0 6 3 2 ) ( x y x y a 2 2 & 1 2 ) ( x y x y b
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EXAMPLE 3 SOLUTION Determine whether the following lines are parallel or perpendicular:- (a) are Parallel (b) are perpendicular (2)(-1/2) = -1 a. b. 9 3 2 3 6 3 2 0 6 3 2 x y x y x y 1 2 1 2 x y x y 4 3 2 3 4 3 4 6 3 6 4 x y x y x y 1 2 1 2 2 2 2 x y x y x y
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Write answers in the slope-intercept form : i) Passes through (2,5) with the slope of ½ ii) Passes through (1,-4) and (-5,4) iii) Perpendicular to the line 2x + y = 3 and passes through (3,5) iv) Parallel to the line 2x - 3y = 5 and passes through (2,-1) EXAMPLE 4 EQUATION OF A LINE 10
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Write answers in the slope-intercept form : i) Passes through (2,5) with the slope of ½ EXAMPLE 4 SOLUTION 11
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Write answers in the slope-intercept form : ii) Passes through (1,-4) and (-5,4) 1) EXAMPLE 4 SOLUTION 12
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Write answers in the slope-intercept form : iii) Perpendicular to the line 2x + y = 3 and passes through (3,5) EXAMPLE 4 EQUATION OF A LINE 13
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iv) Parallel to the line 2x - 3y = 5 and passes through (2,-1) EXAMPLE 4 EQUATION OF A LINE 14
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Example 5 Suppose an art object purchased for $50,000 is expected to appreciate in value at a constant rate of $5000 per year for the next 5 years.
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