Question

A line has a slope of 6/5 and passes through (0,-6) , what is the x-intercept

Answer 1

let's firstly find its equation, and then let's set y = 0, in order to find its x-intercept, keeping in mind that the y-coordinate is 0 of course.

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{6}{5} \\\\\\ \begin{array}c \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}{(-6)}=\stackrel{m}{\cfrac{6}{5}}(x-\stackrel{x_1}{0}) \implies y +6 = \cfrac{6}{5} ( x -0)`

`y+6=\cfrac{6}{5}x\implies \stackrel{\textit{now, setting y = 0}}{0+6=\cfrac{6x}{5}}\implies 6=\cfrac{6x}{5}\implies 30=6x \\\\\\ \cfrac{30}{6}=x\implies 5=x\hspace{5em} {\Large \begin{array}{llll} \stackrel{ x-intercept }{(5~~,~~0)} \end{array}}`