Linear Equations

An equation that can be written of the form

$ ax+b=0,\qquad(a\neq0) $

where $a$ and $b$ are (fixed) real numbers and $x$ is the variable (or the unknown) is called a linear equation. To solve the equation, subtract $b$ from both sides

$ ax+\cancel{b}-\cancel{b} = -b $

and then divide both sides of the resulting equation, $ax=-b$, by $a$:

$ x=-\frac{b}{a} $

(Sometimes, this process is described as "transferring $b$ to the other side of the equation and then "moving the coefficient $a$ to the denominator of $b

quot;.)

• The solution of $ax+b=0$ is the $x$-intercept of the straight line $y=ax+b$ (the $x$-intercept is where the graph intersects the $x$-axis).