Question

Write the equation of each line in slope-intercept form.

The line parallel to y=-3x + 4 that passes through (9,-6).
O y = 3x + 21
Oy=-3x+4
Oy=-1/3x + 27
Oy=-3x + 21

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+4\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 -3 and that it passes through (9 , -6)

`(\stackrel{x_1}{9}~,~\stackrel{y_1}{-6})\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}{(-6)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{9}) \implies y +6= -3 (x -9) \\\\\\ y+6=-3x+27\implies {\LARGE \begin{array}{llll} y=-3x+21 \end{array}}`

Answer 2

The fourth option:

y=-3x+21 is correct.