Straight lines: gradient, intercepts and perpendicularity

Learning objectives

Write the equation of a straight line in the forms y = mx + c, ax + by + d = 0 and y − y₁ = m(x − x₁), and convert between them

Calculate the gradient between two points as (y₂ − y₁)/(x₂ − x₁), and interpret it as a rate of change with units in a modelling context

Use m₁ = m₂ for parallel lines and m₁m₂ = −1 for perpendicular lines to find the equation of a line through a given point

Find the x-intercept and the y-intercept of a line and interpret each in the context of a model, for example as a start value or a break-even point

Find the point of intersection of two lines algebraically or with technology, and interpret it in context