Question

Write an equation in slope-intercept form for the line parallel to y = 2x – 2

that passes through the point (5, -4).

Answer 1

Y = 2x-14
you can use the point slope formula as you have a coordinate given to you. Y - Y1 = m ( X - X1)
Y + 4 = 2 ( X - 5)
Y + 4 = 2X - 10
Y = 2X - 14

Answer 2

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-2\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 al ine whose slope is 2 and passes through (5,-4)

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4}) \qquad \qquad \stackrel{slope}{m}\implies 2 \\\\\\ \begin{array} \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}{2}(x-\stackrel{x_1}{5})\implies y+4=2(x-5) \\\\\\ y+4=2x-10\implies y=2x-14`