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Find the equation of the linear function represented by the table below in slope-intercept form.

x y
-4 17
1 -3
6 -23
11 -43

User WSBT
by
7.5k points

1 Answer

6 votes

well, to get the equation of a line all we need is two points, so let's simply pick two points off the table, hmmmm say (1 , -3) and hmmm (11 , -43)


(\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{11}~,~\stackrel{y_2}{-43}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-43}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{11}-\underset{x_1}{1}}}\implies \cfrac{-43+3}{10}\implies \cfrac{-40}{10}\implies -4


\begin{array}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}{(-3)}=\stackrel{m}{-4}(x-\stackrel{x_1}{1}) \\\\\\ y+3=-4x+4\implies y=-4x+1

User Guilhermecgs
by
8.1k points

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