Question

Find the slope and the intercepts of each line f(x)=2/3x+4

Answer 1

to find the x-intercept of any equation, we simply set y = 0, and then solve for "x".

`\bf \stackrel{f(x)}{0}=\cfrac{2}{3}x+4\implies -4=\cfrac{2x}{3}\implies -12=2x\implies \cfrac{-12}{2}=x\implies -6=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{x-intercept}{(-6,0)}~\hfill`

now to find the y-intercept....hmmm wait just a second, the equation is already in slope-intercept form, therefore,

`\bf \begin{array} \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}~\hspace{7em}f(x)=\stackrel{slope}{\cfrac{2}{3}}x+\stackrel{y-intercept}{4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{y-intercept}{(0,4)}~\hfill`