Find an equation of the line that contains the point $(1,2)$ and is parallel to the line $y=5x$.

Solution  Since the two lines are parallel, the slope of the line we seek equals the slope of the line $y=5x,$ which is $5.$ Since the line we seek also contains the point $( 1,2)$, we use the point-slope form to obtain the equation. $$\begin{eqnarray*} y-y_{1} &=&m( x-x_{1}) \\[0pt] y-2 &=&5( x-1) \\[0pt] y-2 &=&5x-5 \\[0pt] y &=&5x-3 \end{eqnarray*}$$

The line $y=5x-3$ contains the point $( 1,2)$ and is parallel to the line $y=5x.$ See Figure 30.