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1: Straight Lines and Gradients “Teach A Level Maths” Vol. 1: AS Core Modules

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4 2 Finding the Gradient

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The gradient of the straight line joining the points and is e.g. Find the gradient of the straight line joining the points and To use this formula, we don’t need a diagram! Solution:

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Equation of a Straight Line The gradient of the straight line joining the points and is

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Equation of a Straight Line Find the gradient of the line joining the points A(3,–2) and B(–5,6) x 2 = –5y 2 = 6 x 1 = 3 y 1 = –2

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Equation of a Straight Line Find the gradient of the line joining the points A(3,–2) and B(–5,6) x 2 = –5y 2 = 6 x 1 = 3 y 1 = –2

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Equation of a Straight Line c is the point where the line meets the y -axis, the y -intercept and y -intercept, c = e.g. has gradient m = The equation of a straight line is m is the gradient of the line gradient = 2 x intercept on y -axis

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Equation of a Straight Line gradient = 2 x intercept on y -axis ( 4, 7 ) x The coordinates of any point lying on the line satisfy the equation of the line showing that the point ( 4,7 ) lies on the line. e.g. Substituting x = 4 in gives

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Equation of a Straight Line Finding the equation of a straight line when we know e.g.Find the equation of the line with gradient passing through the point its gradient, m and the coordinates of a point on the line (x 1, y 1 ). Solution: So, Using, m is given, so we can find c by substituting for y, m and x. (-1, 3) x Add 2 to both sides C = 5

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Equation of a Straight Line Solution: First find the gradient We could use the 2 nd point, (-1, 3) instead of (2, -3) Using the formula when we are given two points on the line e.g. Find the equation of the line through the points Now use with -3 = -4 + c Add 4 to both sides

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Equation of a Straight Line SUMMARY Equation of a straight line Gradient of a straight line where and are points on the line where m is the gradient and c is the intercept on the y -axis

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Equation of a Straight Line 2. Find the equation of the line through the points Exercise 1. Find the equation of the line with gradient 2 which passes through the point. Solution: So, Solution: So,

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Equation of a Straight Line We sometimes rearrange the equation of a straight line so that zero is on the right-hand side ( r.h.s. ) We must take care with the equation in this form. e.g. can be written as e.g. Find the gradient of the line with equation Solution: Rearranging to the form : so the gradient is

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