Question

Which of the following is the equation of the line that is parallel to y = x + 8 and goes through point (- 10, 4)?

○ y = -x-12
○ y = //x+20²/
○ y = x + 10
○ y=-3x-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 }}{1}x + 8\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're really looking for the equation of a line whose slope is 1 and that it passes through (-10 , 4)

`(\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \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}{4}=\stackrel{m}{ 1}(x-\stackrel{x_1}{(-10)}) \implies y -4= 1 (x +10) \\\\\\ y-4=x+10\implies {\LARGE \begin{array}{llll} y=x+14 \end{array}}`