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1234Linear relations

Theory

Take a look at the applet: Linear Relations

An equation of the form a x + b y = c describes a linear relationship with two variables. The corresponding graph is a straight line. You can find this graph by determining points along this line. This is often done by choosing x = 0 and calculating the corresponding value for y , and by then choosing y = 0 and calculating the corresponding value for x .

Linear equations with two variables such as a x + b y = c can be rewritten as a linear function as long as b 0 .
For example the equation 2 x + 3 y = 6 can be reorganised to give y = - 2 3 x + 2 .
This is then a linear function with -intercept 2 and gradient - 2 3 .

Special cases:

  • a = 0 : the equation then takes on the form b y = c and can be rewritten as y = c b . This is a linear function with gradient 0 .

  • b = 0 : the equation takes on the form a x = c and can be rewritten as x = c a . This is not a linear function as there is no gradient. The graph is a line parallel to the y -axis.

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