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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.