Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Two perpendicular lines have reciprocal and opposite slopes.
First we have to write the given line in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We have this equation:
[tex]x-4y=20[/tex]To write it in the slope-intercept form we have to clear y:
[tex]\begin{gathered} x-20=4y \\ \downarrow \\ y=\frac{1}{4}x-5 \end{gathered}[/tex]The slope is 1/4 and the y-intercept is -5.
The slope of the perpendicular line will be the opposite and reciprocal of 1/4, that's -4.
For now we have the perpendicular line's equation:
[tex]y_p=-4x+b[/tex]There are a lot of lines that are perpendicular to the given line, but only one that passes through (2, -5). We use this point to find the y-intercept by replacing x = 2 and y = -5 into the expression above and solving for b:
[tex]\begin{gathered} -5=-4\cdot2+b \\ -5=-8+b \\ -5+8=b \\ b=3 \end{gathered}[/tex]The y-intercept of the perpendicular line is 3.
The equation of a line perpendicular to the given line that passes through the point (2,-5) is
[tex]y_p=-4x+3[/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
