Question

X 16,24,32 y 44,64,84 what is the y intercept of the line

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{16}~,~\stackrel{y_1}{44})\qquad (\stackrel{x_2}{32}~,~\stackrel{y_2}{84}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{84}-\stackrel{y1}{44}}}{\underset{\textit{\large run}} {\underset{x_2}{32}-\underset{x_1}{16}}} \implies \cfrac{ 40 }{ 16 } \implies \cfrac{ 5 }{ 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}{44}=\stackrel{m}{ \cfrac{ 5 }{ 2 }}(x-\stackrel{x_1}{16})`

now, the y-intercept occurs when x = 0, hmmm what's "y" when x = 0?

`y-44=\cfrac{5}{2}(x-16)\implies \stackrel{ x=0 }{y-44=\cfrac{5}{2}(0-16)}\implies y-44=\cfrac{5(-16)}{2} \\\\\\ y-44=-40\implies y=4\hspace{9em}\underset{ y-intercept }{(\stackrel{x}{0}~~,~~\stackrel{y}{4})}`