1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nikitich [7]
4 years ago
8

Find the equation for the line is perpendicular to 9x+3y=15 (-3,3)

Mathematics
2 answers:
saw5 [17]4 years ago
8 0

well, let's keep in mind that perpendicular lines have negative reciprocal slopes, so hmmm wait a second, what's the slope of the equation above anyway?

\bf 9x+3y=15\implies 3y=-9x+15\implies y=\cfrac{-9x+15}{3}\implies y=\cfrac{-9x}{3}+\cfrac{15}{3} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\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} \\\\[-0.35em] ~\dotfill

\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-3\implies -\cfrac{3}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{3}}}

so then, we're really looking for the equation of a line whose slope is 1/3 and runs through (-3,3)

\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{1}{3} \\\\\\ \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}{\cfrac{1}{3}}[x-\stackrel{x_1}{(-3)}] \\\\\\ y-3=\cfrac{1}{3}(x+3)\implies y-3=\cfrac{1}{3}+1\implies y=\cfrac{1}{3}x+4

a_sh-v [17]4 years ago
4 0

Answer:

-x + 3y = 12.

Step-by-step explanation:

OK. First we need to find the slope of 9x + 3y = 15.

3y = -9x + 15

y = -3x + 5

So it's slope = -3.

Now the slope of the line perpendicular to it is  - 1 / -3 = 1/3.

Now we use the general form point-slope to find the required equation:

y - y1 = m(x - x1)

Here x1 = - 3,  y1 = 3 and m = 1/3:

y - 3 = 1/3(x - -3)

y - 3 =  1`/3(x + 3)

Multiply through by 3:

3y - 9 = x + 3

-x + 3y = 12.

You might be interested in
5^-1 = blank * 5^4 find the missing factor
skad [1K]

Answer:

1/3125 or, 5^-5

Step-by-step explanation:

5^-1 = blank * 5^4

1/5/625= blank   or,     5^-1/5^4=blank

blank=1/3125               5^-5=blank

4 0
3 years ago
Find the next three terms.<br><br> 243, -81, 27, -9...
Katarina [22]

Hi there!


To find the answer, you divide one of the numbers by 3, and some others by -3.


I can show you how to do so! :D


243 ÷ -3 = -81

-81 ÷ 3 = 27

27 ÷ 3 = 9

Next three terms -

9 ÷ 3 = 3

3 ÷ 3 = 1

1 ÷ 3 = 0.3333, the 3 is repeating over and over again


I think this is the answer, based off my notes :)


That's your pattern!


Hope this helps!

Message me if you need anything else, I'd be happy to answer any other questions! :D

4 0
4 years ago
Which angle is supplementary to 4?
Natalija [7]
2 !! hope it helped
8 0
3 years ago
Read 2 more answers
Give P(-1, 8) and Q(5,12), and MN is the image of PQ under a translation of T
Brilliant_brown [7]
Coordinates of N are (-55, 6)
4 0
3 years ago
8th grade math! Help please!
kakasveta [241]
5/21 is the answer to this question.
8 0
4 years ago
Read 2 more answers
Other questions:
  • 0=x^2-4x+3 how many roots does this equation have
    9·1 answer
  • In the box, type the number that will correctly complete the sentence.
    15·1 answer
  • Steve weighs 18 more pounds than Ryan. If their weight totals 144 pounds, how much does Ryan weigh?
    7·2 answers
  • If the monthy cost for 23 HCF is $48.31 , what is the monthly cost for 18 HCF?
    11·1 answer
  • Help help help help help help
    11·1 answer
  • An elephant at the zoo drinks 88 gallons of water each day. The table shows the number of days the elephant drinks water and the
    7·2 answers
  • When a grizzly bear hibernates, its heart rate drops to 10 beats per minute, which is 20% of its normal
    6·2 answers
  • Match the polynomial on the left with the appropriately factored expression on the right.
    13·1 answer
  • 6. The population of wolves is currently 250 in a forest. Scientists estimate that there should be a
    15·1 answer
  • The expression -2(x-4) is the same as?​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!