A graph that forms a straight line is a linear relation; a graph that does not is a non-linear relation. (p.154)
A linear graph can be obtained from a non-linear one by changing the variables on the X-axis, Y-axis or both. (p.154)
Linear graph: Y = mX + c, where m is the gradient and c is the Y-intercept. (p.154)
The line of best fit is a straight line passing through most points, with the remaining points distributed evenly on both sides. (p.156)
The equation of the line of best fit is found using the gradient and Y-intercept (or any two points on the line). (p.157)
Values outside the plotted range can be found by extrapolating the line or using its equation. (p.159)
Gradient is the rate of change of one variable with respect to another; Y-intercept is where the line meets the Y-axis. (p.160)
6.2 Linear Law and Non-Linear Relations
Linear law converts a non-linear relation to the linear form Y = mX + c so a straight line can be drawn. (p.162)
X and Y must contain variables only (not unknown constants); m and c must contain constants only. (p.162)
y = ax + b/x: multiplying by x gives xy = ax2 + b (Y = xy, X = x2, m = a, c = b); dividing by x gives y/x = b(1/x2) + a. (p.162)
y = pqx: log10 y = (log10 q)x + log10 p (Y = log10 y, X = x, m = log10 q, c = log10 p). (p.162)
y = px/q: log10 y = (log10 p)x − log10 q. (p.164)
6.3 Application of Linear Law
Problem steps: convert to linear form, compare with Y = mX + c, build a new table of the new variables, plot and draw the line of best fit, then read the gradient and Y-intercept to find the unknown constants. (p.166)