Question

What is the equation of the line in slope intercept form (1, 10)and (3, 16)

Answer 1

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{16}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{16}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 2 } \implies 3`

`\begin{array} \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}{10}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \\\\\\ y-10=3x-3\implies {\Large \begin{array}{llll} y=3x+7 \end{array}}`

Answer 2

Answer: y= 3x + 7

Explanation:

y2-y1 / x2- x1 (Equation to find slope)

16-10 / 3-1 = 6/2 (Plug in values)

y=3x+b (Plug in value gotten from above)

10 = 3 + b (Plug in values from given point)

y=3x+7 (Answer)