Question

A line is parallel to y= 1/2x +6 and passes through (–8, 0). What is the equation of the line?

Answer 1

keeping in mind that parallel lines have exactly the same slope, hmmm so what's the slope of the equation above?

`\bf y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x+6\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 1/2 and runs through (-8 , 0)

`\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{0})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{1}{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}{0}=\stackrel{m}{\cfrac{1}{2}}[x-\stackrel{x_1}{(-8)}] \\\\\\ y=\cfrac{1}{2}(x+8)\implies y=\cfrac{1}{2}x+4`

Answer 2

y = 1/2x + 4

Explanation:

y = 1/2x + b

0 = -4 + b

b = 4

y = 1/2x + 4