Maths for A Level Chemistry - updated edition

Answers 1 a) Yes: y = 1.4 x + 7 is in the form y = mx + c b) No: y = 4 x 2 + 1 is not in the form y = mx + c as it contains a term in x 2 . c) No: y = 2 x is not in the form y = mx + c d) Yes: y = −4x is in the form y = mx + c with c = 0. e) No: y = √ x is not in the form y = mx + c f) Yes: 2 y = 8x+6 can be divided by 2 to give y = 4 x + 3 which is in the form y = mx + c g) Yes: 5 x + 2 y = 3 can be rearranged to give 2 y = −5 x + 3 and this can be divided by 2 to give y = − 5 2 x + 3 2 which is in the form mx + c h) Yes: y = 4 3 x − 2 is in the form y = mx + c Gradients of straight line graphs Gradients have a sign and a value, so −0.6 is a gradient, as is 4. The sign of the gradient The gradient of a straight line can be positive (if y increases as x increases), negative (if y decreases as x increases) or zero (if the value of y stays the same as x increases). y x 0 Fig 4.1 Positive gradient y x 0 Fig 4.2 Negative gradient y x 0 Fig 4.3 Zero gradient Finding the gradient y x 0 Change in x values Change in y values Fig 4.4 To ϐind the size of the gradient, we draw a triangle like the one formed in Fig 4.4. We then ϐind the distances shown on the diagram and use the following relationship for the gradient: Gradient, m = change in the y -values change in the x -values 4 Graphs 39