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maths 4 Scotland www. maths 4 scotland. co. uk HIGHER MATHS The Straight Line Equation of a straight line Part 4 Next

maths 4 Scotland www. maths 4 scotland. co. uk Unit 1 – Chapter 1 The Straight Line By the end of this lesson you should be able to: • write down the equation of a line given m and c • find the gradient and y-intercept from the equation • find equations of parallel and perpendicular lines • use m = tan to find angles of lines • sketch a line from its equation

maths 4 Scotland www. maths 4 scotland. co. uk Consider the line L with y-intercept c and gradient m L m c O

maths 4 Scotland www. maths 4 scotland. co. uk The line consists of the fixed point A (0, c) and the set of points P(x, y) for which L m c O A P

maths 4 Scotland www. maths 4 scotland. co. uk This is also known as the locus of point P(x, y) where L m c O A P

maths 4 Scotland www. maths 4 scotland. co. uk Note Equation of a line The equation of a line with gradient m and y-intercept c L m c P A O If x = 0 then y = c, giving point A So, L is the set of points for which

maths 4 Scotland www. maths 4 scotland. co. uk Example: Find the equation of the line which passes through (0, 2) with gradient of 3 2 O m=3

maths 4 Scotland www. maths 4 scotland. co. uk Example: Find the gradient and y-intercept of the line with equation m c

maths 4 Scotland www. maths 4 scotland. co. uk Example: Find the equation of the line parallel to and passing through (0, 4) x x

maths 4 Scotland www. maths 4 scotland. co. uk Example: Find the equation of the line perpendicular to and passing through (0, 3)

maths 4 Scotland www. maths 4 scotland. co. uk Example: Sketch the line with equation 1 x

maths 4 Scotland www. maths 4 scotland. co. uk Example: Find the equation of the line which makes an angle of 135° with OX and passes through (0, 5) 5 m = -1 135° O X

maths 4 Scotland Example: www. maths 4 scotland. co. uk Do these points lie on the line i) (3, 2) ii) ( 1, 6) If a point lies on a line then it will satisfy the equation of the line i) 5 (3, 2) x=3 m = 1 135° O X (3, -2) does NOT lie on line

maths 4 Scotland Example: www. maths 4 scotland. co. uk Do these points lie on the line: i) (3, -2) ii) (-1, 6) If a point lies on a line then it will satisfy the equation of the line ii) 5 (-1, 6) x = -1 m = -1 135° O X (-1, 6) does lie on line

maths 4 Scotland www. maths 4 scotland. co. uk Note Equation of a line If a point lies on a line then it will satisfy the equation of the line i. e. the equation will be true If the equation of a straight line is in the form then gradient = m y-intercept = c

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