Question

Write an equation of the line passing through point P (0, 1)$ that is parallel to the line y=-2x+3

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 }}{-2}x+3\qquad \impliedby \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're really looking for the equation of a line whose slope is -2 and that it passes through (0 , 1)

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \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}{1}=\stackrel{m}{- 2}(x-\stackrel{x_1}{0})\implies {\LARGE \begin{array}{llll} y=-2x+1 \end{array}}`