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**“Teach A Level Maths” Vol. 1: AS Core Modules**

1: Straight Lines and Gradients

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Finding the Gradient 4 2

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**is The gradient of the straight line joining the points and**

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

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**The gradient of the straight line joining the points**

and is

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**Find the gradient of the line joining the points A(3,–2) and B(–5,6)**

x1= 3 y1= –2 x2 = –5 y2 = 6

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**Find the gradient of the line joining the points A(3,–2) and B(–5,6)**

x1 = 3 y1= –2 x2 = –5 y2 = 6

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**m is the gradient of the line **

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

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**e.g. Substituting x = 4 in gives**

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 e.g. Substituting x = 4 in gives showing that the point ( 4,7 ) lies on the line.

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**Finding the equation of a straight line when we know**

its gradient, m and the coordinates of a point on the line (x1,y1). Using , m is given, so we can find c by substituting for y, m and x. e.g. Find the equation of the line with gradient passing through the point Solution: (-1, 3) x Add 2 to both sides C = 5 So,

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**Using the formula when we are given two points on the line**

e.g. Find the equation of the line through the points Solution: First find the gradient Now use with We could use the 2nd point, (-1, 3) instead of (2, -3) Add 4 to both sides -3 = -4 + c

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

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

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

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