Chapter 16 Graphs

Learning Outcomes Draw straight line graphs Draw special horizontal & vertical graphs Recognise the gradient & y-intercept from an equation Find equations of lines with given gradients & y-intercepts Answer questions from given straight line graphs Re-arrange equations to find the gradient & y-intercept Use graphs to solve equations Use graphs to represent real-life scenarios

Drawing Straight Line Graphs Special Graphs x = 3 x = -9 y = 3 y = -5 y = x

Drawing Straight Line Graphs Pick 3 x-values and work out the y- values y = 2x + 1 y = 3x – 4 y = 5 – 2x

Gradient & y-intercept The gradient is the steepness of the line and is represented by m A positive gradient points up A negative gradient point down The y-intercept is where it crosses the y- axis and is represented by c The general form of any straight line is: y = mx + c

General Equation of Straight Line Examples 1. Write down the gradient & y-intercept of: (a) y = 2x + 3 (b) y = -3x -5 (c) y = 7 - x 2. Find the equation of a line through (0, -3) with gradient 4

Re-arranging Equations Before finding the gradient & y-intercept you must have the equation in the form y = mx + c Example Find the gradient & y-intercept and sketch the graph in: (a) 4y – 3x = 8 (b) 2x + 5y = 0 (c) 2y + 3x = 4

Using Graphs to Solve Equations Examples 1. Draw the graphs of y = 2 and y = 2x – 3 and solve 2x – 3 = 2

Using Graphs to Solve Equations Examples 2. Draw the graphs of y = ½x and y = 3-2x and solve ½x = 3 – 2x