Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Answer:
y=-1/4x+9/4
Step-by-step explanation:
Get slope of the line first (to find slope that is perpendicular, get the negative reciprocal)
4 turns into -1/4
To get the y-intercept, plug in the given coordinate values into this formula:
y=mx+b
3=-3(-1/4)+b
3-3/4=b
b=9/4
b is our y-intercept
9/4 is our y-intercept
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = 4 + x\implies y = \stackrel{\stackrel{m}{\downarrow }}{1}x+4\qquad \impliedby \begin{array}{|c|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}[/tex]
so therefore
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies\cfrac{1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{1}\implies -1}}[/tex]
so we're really looking for the equation of a line whose slope is -1 and passes through (-3 , 3)
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -1 \\\\\\ \begin{array}{|c|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}{3}=\stackrel{m}{-1}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-3=-(x+3)\implies y-3 = -x-3\implies y = -x[/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
