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# Linear equations

### What are linear equations?

- Linear equations contain variables to a power of one. For example, variables could be \(x\) and \(y\) but not \(x^{2}\) or \(y^{3}\).
- They do not contain products of variables. For example, \(xy\,,\ yz\,,\ xyz\) are not allowed.
- Examples of linear and nonlinear equations:
- \(x + 2 = 5\) is a linear equation
- \(3x - 4y = -1\) is a linear equation
- \(x^{2} + 2 = 5\) is a nonlinear equation
- \(xy + 3 = 7\) is a nonlinear equation

- The most commonly used is the linear equation for a straight line \[y=mx+c\] where \(m\) is the slope or gradient of the line and \(c\) is the \(y\)-intercept.