Question

write the point slope form and then the slope intercept form of the equation of the line through the given point with the given slope. through: ( 4, 5 ), slope = 1/2

Answer 1

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2}`

`\begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y-5=\cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x+3\impliedby \begin{array}ll \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}`