Straight-line graphs and linearising relationships

Learning objectives

Find the gradient, the midpoint and the length of a line segment joining two points, and write the equation of a line in the form y = mx + c or ax + by = d

Use the conditions m₁ = m₂ for parallel lines and m₁m₂ = −1 for perpendicular lines to find equations of parallel lines, perpendicular lines and perpendicular bisectors

Transform a relationship of the form y = axⁿ into the linear form lg y = n lg x + lg a, and a relationship of the form y = Abˣ into lg y = (lg b)x + lg A, choosing the correct quantities to plot on each axis

Read the gradient and the intercept from a straight-line graph drawn from experimental data and convert them back into the constants of the original non-linear relationship

Use a linearised graph to estimate values, and decide from how well the plotted points lie on a straight line whether the proposed model fits the data

Solve area and geometry problems set on a coordinate grid, such as finding the fourth vertex of a parallelogram or the area of a triangle from its vertices