Question

Write the linear equation that gives the rule for this table. x 5,6,7,8 and y 15,18,21,24

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}{6}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{24}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{24}-\stackrel{y1}{18}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{6}}} \implies \cfrac{ 6 }{ 2 } \implies 3`

`\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}{18}=\stackrel{m}{3}(x-\stackrel{x_1}{6}) \\\\\\ y-18=3x-18\implies {\Large \begin{array}{llll} y=3x \end{array}}`