Question

Write and Equation of a line in point-slope form that is parrallel to y=2x-1 and goes through the point (-2,5)

Answer 1

keeping in mind that parallel lines have exactly the same slope, hmm what's the slope of the equation above.

`\bf y = \stackrel{\stackrel{m}{\downarrow }}{2}x-1\qquad \impliedby \begin{array}c \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 runs through (-2,5)

`\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})~\hspace{10em} \stackrel{slope}{m}\implies 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}{5}=\stackrel{m}{2}[x-\stackrel{x_1}{(-2)}]\implies y-5=2(x+2)`