Finding an Equation of a Line that Is Parallel to a Given Line

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.