Writing Equations of Parallel Lines

Parallel lines have the same slope which means that the coefficient in front of $x$, which is their slope, is the same. We can start by simplifying the fractions. Both $\frac{18}{20}$ and $\frac{2}{4}$ can be simplified by dividing by $2.$ $$\frac{2/2}{4/2}=\frac{1}{2}\text{and}\frac{18/2}{20/2}=\frac{9}{10}$$ In order to more easily compare with the other equations' slopes, write the fractions as a decimal number. $$\frac{9}{10}=0.9,\frac{3}{4}=0.75\text{and}\frac{1}{2}=0.5$$ Write out all the equations with their $m$-values as decimals. $$y_1=0.5x+50y_2=0.9x-1y_3=0.75x+2$$ $$y_4=0.9x-11y_5=0.75x+11y_6=0.5x+700$$ Now, we can see which lines have the same slopes. $$\begin{array}{rl}& y_1\text{and}{y}_6\\ & y_2\text{and}{y}_4\\ & y_3\text{and}{y}_5\end{array}$$