Question

Determine the equation of the line for the given information: The graph has y-intercept (0, 6) and contains the point (2, 1). a. y = 2.5 x + 6 b. y = negative 2.5 x + 6 c. y = 6 x + negative 2.5 d. y = 2 x + 6

Answer 1

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{ -5 }{ 2 } \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}{6}=\stackrel{m}{-\cfrac{5}{2}}(x-\stackrel{x_1}{0}) \\\\\\ y-6=-\cfrac{5}{2}x\implies y=-\cfrac{5}{2}+6\implies {\Large \begin{array}{llll} y=-2.5x+6 \end{array}}`