Question

Write the equation for the following relationships

x: 1/2, 0, 2
y: 4, 0, 16

please write in the y=mx+b formula

Answer 1

to get the equation of any straight line we simply need two points off of it, from the table
`\begin{array}cccc \cline{1-4} x&(1)/(2)&0&2\\ \cline{1-4} y&4&0&16\\ \cline{1-4} \end{array}` let's use the points of (0 , 0) and (2 , 16)

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{16}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{16}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}}\implies \cfrac{16}{2}\implies 8 \\\\\\ \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}{0}=\stackrel{m}{8}(x-\stackrel{x_1}{0})\implies y=8x`