Question

Question 12
Write an equation of a line that passes through (8,5) and (11, 14).

Answer 1

So to write this as an equation follow the steps:

1.First you take y delta divided by x delta. This means that you but in the coordinates, take them minus eachother then divided by eachother. Let me show you with maths for better understanding:

Now you have k in y=kx+m ( the equation has different letters depening on where you are from but I think you understand).

So know we just use simple algebra bu putting in the coordinates in the equation. So for this example im going to use the coordinates x= 8 and y=5

so we get:

Answer 2

`(\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{11}~,~\stackrel{y_2}{14})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{11}-\underset{x_1}{8}}} \implies \cfrac{14 -5}{11 -8} \implies \cfrac{ 9 }{ 3 }\implies 3`

`\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}{5}=\stackrel{m}{3}(x-\stackrel{x_1}{8}) \\\\\\ y-5=3x-24\implies y=3x-19`