Rewriting a formula for a different variable
The area of a trapezoid is resented by the formula $A=\frac{1}{2}(b_1+b_2)h$.
I want draw several trapezoids, all with the same Area (to be decided later), as I change the bases I need to know what height to draw the trapezoid. To make the math easier I will re-write the formula for height ($h$).
\[ \begin{align*}
A &= \frac{1}{2}(b_1+b_2)h \\
\\
\color{blue}{2 *} A &= \color{blue}{2 *} \frac{1}{2}(b_1+b_2)h \\
\\
2A &= (b_1+b_2)h \\
\\
\frac{2A}{\color{blue}{(b_1+b_2)}} &= \frac{(b_1+b_2)}{\color{blue}{(b_1+b_2)}}h \\
\\
\color{red}{\frac{2A}{(b_1+b_2)}} &= \color{red}{h} \\
\end{align*}\]
Rewriting an equation for a different variable
Often when graphing an equation it is useful to solve for y
(also known as $y-intercept$ form.)
ex. Re-write the equation $3y-5x=12$ in $y-intercept$ form.
\[ \begin{align*}
3y-5x &= 12 \\
\\
3y-5x \color{blue}{-5x} &= \color{blue}{{}^-5x} + 12 \\
\\
3y &= {}^-5x+12 \\
\\
\frac{3y}{\color{blue}{3}} &= \frac{{}^-5x}{\color{blue}{3}}+\frac{12}{\color{blue}{3}} \\
\\
\color{red}{y} &= \color{red}{\frac{{}^-5x}{3} + 4 }
\end{align*}\]
