Question

Determine the x and yintercepts of the line that correspond to the following table of values. (-7,7) (-5,0) (-3,-7)

Answer 1

let's pick any two points off that table to get its slope.

`\bf \begin{array} \cline{1-2} x&y\\ \cline{1-2} -7&7\\ -5&0\\ -3&-7\\ \cline{1-2} \end{array}~\hspace{7em} (\stackrel{x_1}{-7}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-7-7}{-3-(-7)}\implies \cfrac{-14}{-3+7}\implies \cfrac{-14}{4}\implies -\cfrac{7}{2}`

`\bf \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-7=-\cfrac{7}{2}[x-(-7)]\implies y-7=-\cfrac{7}{2}(x+7) \\\\\\ y-7=-\cfrac{7}{2}x-\cfrac{49}{2}\implies y=-\cfrac{7}{2}x-\cfrac{49}{2}+7`

`\bf y=-\cfrac{7}{2}x+\cfrac{-49+14}{2}\implies y=-\cfrac{7}{2}x\stackrel{\stackrel{\left( 0~,~-(35)/(2) \right)}{\downarrow }}{-\cfrac{35}{2}}\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}`