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## Mathematics

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**y**x O Mathematics Title: Equations of Straight Line**Slope of AB =**Slope of PA = Two-Point Form y Given a straight line which passes through the points A and B, then x x x If P(x, y) is any point on the line AB, then x O**=**Since PA and AB are parts of the same straight line, then Slope of PA = Slope of AB i.e. This equation is known as the Two-Point Form of the straight line. (Go to Example 1)**y**Slope of PA = x O Point-Slope Form Given a straight line which passes through the point A and has m as its slope. x Slope = m If P(x, y) is any point on the line , then x**= m**Since slope of PA equals to the slope of the straight line, then i.e. This equation is known as the Point-Slope Form of the straight line. (Go to Example 2)**y**x O Slope of PA = Slope-Intercept Form Given a straight line which cuts the y-axis at A and with slope m . (Note: c is called the y-intercept of the straight line.) x P(x, y) A(0, c) x c If P is any point on the line, then Slope = m**Since slope of PA is equal to the slope of the line, then by**Point-Slope Form (y - c) = m(x – 0) y = mx + c i.e. This equation is known as the Slope-Intercept Form of the straight line. (Go to Example 3)**y**Slope of AB = = x O Slope of PA = Intercept Form Given a straight line which cuts the x-axis at A and y-axis at B. (Note: a is called the x-intercept of the straight line.) B(0, b) x P(x, y) b x A(a, 0) x a If P is any point on the line, then**=**Since the slope of PA equals to the slope of AB, then bx + ay = ab Dividing both sides by ab, we have This equation is known as the Intercept Form of the straight line. (Go to Example 4)**Standard Form**It should be noted that all the different standard forms of the equation of a straight line can be reduced to the form Ax + By + C = 0 where A, B and C are constants with A and B not both zero. This equation is known as the Standard Form of a straight line.**y**x O Mathematics Linear Equations**y**x O Example 1 (Two-Point Form) Find the equation of the straight line. B(5, 6) x The required equation: x x A(1, 3) 4(y – 3) = 3(x – 1) i.e. 3x – 4y + 9 = 0 (Note: The answer is in General Form)**y**x O Example 2 (Point-Slope Form) Find the equation of the straight line. x Slope = 2 P(x, y) The required equation: y – 3 = 2(x – 1) x A(1, 3) i.e. 2x – y + 1 = 0 (Note: The answer is in General Form)**y**x O Example 3 (Slope-Intercept Form) Find the equation of the straight line. P(x, y) x The required equation: A(0, 4) x y = 2x + 4 i.e. 2x – y + 4 = 0 Slope = 2 (Note: The answer is in General Form)**y**x O Example 4 (Standard Form) Find the equation of the straight line. The required equation: B(0, 5) x P(x, y) 5x + 7y = 35 x A(7, 0) i.e. 5x + 7y – 35 = 0 x (Note: The answer is in Standard Form)