Question

What is the equation of the line that passes thru (1,-2) and is parallel to y = 3/4x + 2

Answer 1

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

`y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{4}}x+2\qquad \impliedby \qquad \begin{array} \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}`

so we are really looking for the equation of a line whose slope is 3/4 and it passes through (1 , -2
`(\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{3}{4} \\\\\\ \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}{(-2)}=\stackrel{m}{\cfrac{3}{4}}(x-\stackrel{x_1}{1}) \implies y +2 = \cfrac{3}{4} ( x -1) \\\\\\ y+2=\cfrac{3}{4}x-\cfrac{3}{4}\implies y=\cfrac{3}{4}x-\cfrac{3}{4}-2\implies {\Large \begin{array}{llll} y=\cfrac{3}{4}x-\cfrac{11}{4} \end{array}}`)