Question

Write an equation of the line that passes through (1, 1) and (3, 3).

Answer 1

Answer: y=x+2

Step-by-step explanation: to find the slope use the formula y2-y1/x2-x1 which will get 3-1/3-1= 2/2= 1 so the slope is one. then take formula (y-y1)=m(x-x1) m is slope so you will get (y-3)=1(x-1) distribute the one y-3=x-1 add three to both sides to get y=x+2

Answer 2

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\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}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 2 }{ 2 } \implies 1`

`\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}{1}=\stackrel{m}{ 1}(x-\stackrel{x_1}{1})\implies y-1=x-1\implies \boxed{y=x}`