Question

Write the equation of the line shown​

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}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{6 +2}{3 +3} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{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}{(-2)}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{(-3)}) \implies y +2 = \cfrac{4}{3} ( x +3) \\\\\\ y+2=\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=\cfrac{4}{3}x+2 \end{array}}`

Answer 2

y = 4/3x + 2

Explanation:

Firstly, we need to remember that linear functions are written as y = mx + b, m being slope and b the y-intercept. To find slope, you can use rise/run using the slope formula or just counting the spaces. Then, for the y-intercept, you just need to look for where the function touches the y-axis when x = 0.