Question

Work out the equation of the line shown below

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}{10}~,~\stackrel{y_1}{20})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{140}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{140}-\stackrel{y1}{20}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{10}}} \implies \cfrac{ 120 }{ 20 } \implies 6`

`\begin{array}c \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}{20}=\stackrel{m}{6}(x-\stackrel{x_1}{10}) \\\\\\ y-20=6x-60\implies {\Large \begin{array}{llll} y=6x-40 \end{array}}`

Answer 2

The equation of the line is y = 6x - 40, where the slope (m) is 6 and the y-intercept (c) is -40.

The equation of the line shown in the picture is y = 6x - 40.

To find this equation, we add 20 to both sides of the given equation y - 20 = 6x - 60 to isolate the term with y. Simplifying both sides gives us the equation y = 6x - 40,

where the slope (m) is 6 and the y-intercept (c) is -40.