Question

Write an equation in slope-intercept form using the given information about the line. No spaces, decimals, or mixed numbers. Write fractions in the form a/b.
It passes through the points (4, 9) and (2, 8).

y= ?

Answer 1

$(\stackrel{x_1}{4}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}}\implies \cfrac{-1}{-2}\implies \cfrac{1}{2}$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y-9=\cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x+7$