• To recognise a linear function. • To be able to use both forms of an equation of a straight line: y = mx + c and ( y − y1) = m (x − x1). • To be able to fi nd the equation of a straight line from its graph.
• To be able to fi nd the intercepts of a straight line on the axes. • To recognise the equations of straight lines that are parallel to the axes.
• To plot intersecting linear functions fi nding where they intersect both graphically and algebraically.
• To use linear functions to solve real-life problems. 16.1 What is a linear function?
A linear function is a relation between two variables x and y that can be written in the form: y = f (x) = mx + c or y = f (x) = ax + b, where m, c, a, b ∈ are constant real numbers. The equations are both forms of the equation of a straight line and so the graph of y against x is a straight-line graph.
m (or a) is called the coeffi cient of x. c (or b) is called the constant term.
EXAMPLE 1
Write the following in the form y = mx + c and hence write down the values of m and c:
(a) 3y = 7x – 11
Solution (a) 3y = 7x – 11 y = 7
_ 3 x − 11
m = 7 _
(b) 2x + y = 0
(b) 2x + y = 0 y = –2x + 0 m = –2, c = 0
m is the slope of the line and c is its intercept on the y-axis.
