How to graph an algebraic expression in the format of y=mx+b?

Wednesday, May 14, 2014

How to graph an algebraic expression in the format of y=mx+b?

Hello!

This is the equation of a straight line in the so-called "slope-intercept form". It is a useful form, although it cannot represent vertical lines (they have equations of the form $\displaystyle{x}={a}$ ).

Here $\displaystyle{b}$ is the y-intercept (a value of $\displaystyle{y}$ for $\displaystyle{x}={0}$ ) and $\displaystyle{m}$ is the slope (the tangent of the angle of incline with respect to the x-axis).

The simplest way to draw a straight line is to find two distinct points on it and apply a ruler. One point is almost given, it has the coordinates $\displaystyle{\left({0},{b}\right)}.$ The second point may be obtained for, say, $\displaystyle{x}={1}:$ $\displaystyle{\left({1},{m}+{b}\right)}.$ The other way is to find the x-intercept, the point $\displaystyle{x}$ where $\displaystyle{y}={m}{x}+{b}={0}.$ For $\displaystyle{m}\ne{0}$ it is $\displaystyle-\frac{{b}}{{m}},$ so the second point is $\displaystyle{\left(-\frac{{b}}{{m}},{0}\right)}.$ For $\displaystyle{m}={0}$ the line is parallel to the x-axis.