Question

5 points

Select the equation in slope-intercept form for the line through points (8,5) and (4.-3) and is parallel to the line described by y = 2x - 5

A. y=-2x+9

B. y=-2x-7

C. y=2x+12

D. y=2x-11

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-5\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 passes through (4 , -3)

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad \qquad \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}{(-3)}=\stackrel{m}{2}(x-\stackrel{x_1}{4}) \\\\\\ y+3=2x-8\implies y=2x-11`