OCR GCSE MATHS 8.4 AND 8.5 GRAPHS AND THEIR EQUATIONS>GUARANTEED SUCCES

8.4 and 8.5 Graphs and their equations ©Cambridge University Press and OCR 2021 1 8 Equations 8.4 and 8.5 Graphs and their equations • linear equations • two linear simultaneous equations • quadratic equations • real life graphs. Linear equation graphs WORKED EXAMPLES This is the graph of y = 2 − 4x. a Use the graph to find the value of y when i x = 0 ii x = 1 iii x = 2 b What is the value of x when y = −4? Solution a Each point on the graph can be written as coordinates. i When x = 0, y = 2 (since the point (0, 2) lies on the graph). ii When x = 1, y = −2 (since the point (1, −2) lies on the graph). iii When x = 2, y = −6 (since the point (2, −6) lies on the graph). 8.4 and 8.5 Graphs and their equations ©Cambridge University Press and OCR 2021 2 b Find −4 on the y-axis. Draw a horizontal straight line to the graph and then a vertical straight line up to the x-axis. Write down this value of x. The answer is x = 1.5. Exercise 1 TIP When you solve an equation, you are finding its solution(s). Another name for solution(s) is root(s). 1 Use this graph of the equation y = 3x − 2 to find the value of y for the following values. a x = 0 b x = 1 c x = 2 8.4 and 8.5 Graphs and their equations ©Cambridge University Press and OCR 2021 3 2 Use this graph of the equation y = 2x + 2 to find the value of x for the following values. a y = −4 b y = 0 c y = 4 Two linear (simultaneous) equations WORKED EXAMPLE The diagram shows the graphs of two linear equations, y = 2x and y = −2x + 8. Use the graph to find the solution to the two equations. Solution The x and y coordinates of the intersection of the lines is the same as the solution to the simultaneous equations if solved algebraically. In this case, the coordinates where the two lines cross is (2, 4), so the solution to the two equations is x = 2 and y = 4. 8.4 and 8.5 Graphs and their equations ©Cambridge University Press and OCR 2021 4 Exercise 2 1 These lines have equations: 2y + 3x = 12 and 2y − x = 4 Use the graph to find the solution to the equations if solved simultaneously