Using the Point-Slope Form of a Line

An equation of the line with slope \(4\) and containing the point \(( 1,2)\) can be found by using the point-slope form with \(m=4\), \(x_{1}=1\), and \(y_{1}=2\). \[ \begin{array}{lrcll@{{16pt}}ll} & y-y_{1}&=&m( x-x_{1}) & & {\color{#0066A7}{\hbox{Point-slope form of a line}}} & \\[3pt] & y-2&=&4( x-1) & & {\color{#0066A7}{{m=4}\hbox{, }{x}_{1}{=1} \hbox{, }{y}_{1}{=2}}} & \\[3pt] \,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ & ~\ \ \ \ \ y&=&4x-2 & & {\color{#0066A7}{\hbox{ Solve for }{y.}}} & \hbox{ } \end{array} \]

See Figure 28 for the graph of \(y\).