Linear FunctionsWhat Is a Straight Line?

A straight line is the simplest function in mathematics: every step you take sideways changes the height by the same fixed amount. We can capture any straight line with a single equation,

where m is the slope (how steep the line is) and c is the y-intercept (where the line crosses the vertical axis). This marriage of algebra and geometry reaches back to al-Khwarizmi, whose work gave algebra its name, and to Descartes, who first plotted equations on a grid.

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Every letter in has a job. The number multiplying the independent variable x is the slope; the number on its own is the intercept.

If a line has equation , then its slope is and it crosses the y-axis at height .

A line with a bigger slope is steeperflatterexactly as steep.

Which of these equations is not a straight line?

Which equation has the steepest slope?

(A)

(B)

(C)