Question

Find an equation of the line passing through the given points. Use function notation to write the equation. (-3,11) and (0,2)

Answer 1

`\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-11}{0-(-3)}\implies \cfrac{-9}{0+3}\implies \cfrac{-9}{3}\implies -3 \\\\\\`

`\bf \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-11=-3[x-(-3)]\implies y-11=-3(x+3) \\\\\\ y-11=-3x-9\implies y=-3x+2\implies \stackrel{\textit{using function notation}}{f(x)=-3x+2}`

Answer 2

y=-3x+2

Explanation: