Question

Write a linear function that relates y to x .

X 0 1.5 3 4.5
Y 5 4 3 2
Y=

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those in the picture below.

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{0}}} \implies \cfrac{ -2 }{ 3 } \implies - \cfrac{ 2 }{ 3 }`

`\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}{5}=\stackrel{m}{- \cfrac{ 2 }{ 3 }}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=-\cfrac{2}{3}x+5 \end{array}}`