Question

Line A passes through the point (4, 17) and is parallel to the line given

by y = 3x + 9.
What is the equation of line A?
Give your answer in the form y = mx + c, where m and c are integers
or fractions in their simplest forms.

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 }}{3}x+9\impliedby \begin{array}ll \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 are really looking for the equation of a line whose slope is 3 and it passes through (4 , 17)

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{17})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}ll \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}{17}=\stackrel{m}{3}(x-\stackrel{x_1}{4}) \\\\\\ y -17 = 3 x -12 \implies {\Large \begin{array}{llll} y = 3 x +5 \end{array}}`