Step-by-step explanation:
Given points are:
[tex] (-1,\:3)=(x_1,\: y_1) \:\&\:(1, \:7)=(x_2,\:y_2) [/tex]
Equation of line in two point form is given as:
[tex] \frac{y-y_1 }{y_1 - y_2} = \frac{x-x_1 }{x_1 - x_2} \\ \\ \therefore \: \frac{y - 3}{3 - 7} = \frac{x - ( - 1)}{ - 1 - 1} \\ \\ \therefore \: \frac{y - 3}{ - 4} = \frac{x + 1}{ - 2} \\ \\ \therefore \: \frac{y - 3}{ 2} = \frac{x + 1}{ 1} \\ \\ \huge \purple{ \boxed{\therefore \:y - 3 = 2(x + 1)}} \\ this \: is \: the \: equation \: of \: line \: in \: \\ point - slope \: form.\\simplifying \: it \: further \: we \: find: \\ y - 3 = 2x + 2 \\ \\ \therefore \:y = 2x + 2 + 3 \\ \\ \huge \red{ \boxed{\therefore \:y = 2x + 5}} \\ this \: is \: the \: equation \: of \: line \: in \: \\ slope - intercept \: form.[/tex]
