How do I approach solving linear function problems?
In this post, we will model, analyse and solve problems involving linear functions, as a part of the Prelim Maths Advanced course under the topic Working with Functions and sub-part Linear, Quadratic and Cubic Functions, specifically focusing on solving linear function problems. We will:
- Recognise that a direct variation relationship produces a straight-line graph
- Explain the geometrical significance of and in the equation f(x) = mx + b
- Derive the equation of a straight line passing through a fixed point (x_{1},y_{1}) and having a given gradient using the formula y - y_{1} = m(x - x_{1})
- Derive the equation of a straight line passing through two points (x_{1},y_{1}) and (x_{2},y_{2}) by first calculating its gradient using the formula m = (y_{2} - y_{1})/(x_{2} - x_{1})
- Understand and use the fact that parallel lines have the same gradient and that two lines with gradient m_{1} and m_{2} respectively are perpendicular if and only if m_{1} \times m_{2}
- Find the equations of straight lines, including parallel and perpendicular lines, given sufficient information
How do I solve and model linear functions?
This video provides a large amount of worked examples of linear functions, which require the equations of f(x) = mx + b , y - y_{1} = m(x - x_{1}) and m = (y_{2} - y_{1})/(x_{2} - x_{1}) to solve.
This video explains how to write equations of parallel and perpendicular lines, giving worked examples of problems requiring the equations of m_{1} \times m_{2}
