Maths for A Level Chemistry - updated edition

Note that we have to look at which way the line slopes to determine whether the gradient of the line is positive or negative. We only include the sign, if the gradient is negative. If the gradient is positive, say 4, then we do not write +4. 0 2 4 6 8 10 x 14 12 10 8 6 4 2 0 y Change in x values = 8 Change in y values = 6 Fig 4.5 Fig 4.5 shows a straight line graph. In order to ϐind the gradient of this graph we need to ϐind a convenient place to construct a triangle. We try to ϐind a place where the graph cuts through one of the corners of one of the large squares on the grid. It is more accurate if the triangle is made as large as convenient. You can see that the points (0, 6) and (8, 12) are convenient points to start and ϐinish the triangle. From the graph you can see that the two distances are 6 and 8. Notice that for the line y increases as x increases so the gradient is positive. We then use, gradient, m = change in the y -values change in the x -values = 6 8 = 3 4 or 0.75 4.2 Linear relationships A linear relationship is one in the form y = mx + c , where x and y are the variables and m is the gradient of the line and c is the intercept of the line on the y- axis. If a graph of a quantity plotted on the y- axis against a quantity plotted on the x- axis is a straight line, then the two quantities are linearly related. Take the following straight line, for example 0 5 10 15 20 25 x 50 40 30 20 10 0 y 20 30 Mathematics for Chemistry 40