Edexcel Pure Maths Chapter 5|2023 LATEST UPDATE|GUARANTEED SUCCESS

How to calculate the gradient of a line joining 2 points y2-y1 / x2-x1 What are two ways of writing the equations of lines? -y=mx+c, where m is the gradient and c is the y intercept -ax+by+c, where a b and c are integers How can you define a straight line? By giving: one point on the line and the gradient, or two different points on the line How to write the equation of the line with the gradient m that passes through (x1,y1) y-y1=m(x-1) What do parallel lines have? The same gradient What does a trapezium have? Exactly one pair of parallel sides What are perpendicular lines? Lines at right angles to each other. If one line has a gradient m, a perpendicular line has a gradient -1/m. The product of two perpendicular lines gradients are -1 How to find the distance between two points √(x2-x1)^2 + (y2-y1)^2 What does it mean if two line segments are congruent? They are the same length What's the shortest distance between two parallel lines? The perpendicular distance between them When are two quantities in direct proportion? When they increase at the same rate-graph would be a straight line through the origin. y=kx When can you use a linear model? To show the relationship between two variables, x and y. The graph of a linear model is a straight line, and the variables are related by an equation of the form y=mx+b Can a linear model still be appropriate even if all the points don't lie directly on the line? Yes-they should still be close to the line, but the further away they are the less appropriate a linear model is for the data