Respuesta :
[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{4}{5}}x+2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
keeping in mind that parallel lines have the same exact slope, thus we're really looking for a the equation of a line whose sloope is 4/5 and runs through (1,2),
[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{2})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{4}{5} \\\\\\ \begin{array}{|c|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}{5}}(x-\stackrel{x_1}{1}) \\\\\\ y-2=\cfrac{4}{5}x-\cfrac{4}{5}\implies y=\cfrac{4}{5}x-\cfrac{4}{5}+2\implies y=\cfrac{4}{5}x+\cfrac{6}{5}[/tex]
Two lines are said to be parallel if they have the same slope. The equation of the line parallel to [tex]y = \frac{4}{5}x + 2[/tex] and passes through [tex](1,2)[/tex]is: [tex]y =\frac{4}{5}x + \frac{6}{5}[/tex]
Given that
[tex]y = \frac{4}{5}x + 2[/tex]
A linear equation is represented as:
[tex]y = mx + c[/tex]
Where
[tex]m \to slope[/tex]
So, the slope of [tex]y = \frac{4}{5}x + 2[/tex] is:
[tex]m = \frac{4}{5}[/tex]
When two lines are parallel, they have the same slope.
This means that the line that passes through [tex](1,2)[/tex] has the same slope as [tex]y = \frac{4}{5}x + 2[/tex]
i.e. [tex]m = \frac{4}{5}[/tex]
The equation of the line is calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where:
[tex](x_1,y_1) = (1,2)[/tex]
So, we have:
[tex]y =\frac{4}{5}(x - 1) + 2[/tex]
Open bracket
[tex]y =\frac{4}{5}x - \frac{4}{5} + 2[/tex]
Take LCM
[tex]y =\frac{4}{5}x + \frac{-4+10}{5}[/tex]
[tex]y =\frac{4}{5}x + \frac{6}{5}[/tex]
Hence, the equation of the line is: [tex]y =\frac{4}{5}x + \frac{6}{5}[/tex]
Read more about equation of lines at:
https://brainly.com/question/2564656
