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
Vika [28.1K]
3 years ago
10

Write an equation of the line that passes through (−3,3) and is perpendicular to the line 2y=8x−6.

Mathematics
2 answers:
fiasKO [112]3 years ago
6 0

Answer:

4y = -x + 9

Step-by-step explanation:

2y = 8x - 6

Divide through by 2:-

y = 4x -3   so the slope of this line  = 4

Slope of the line perpendicular to this  = -1/4

So using the point/slope form of an equation of a line and the point (-3,3) we have:-

y  - 3 =  -1/4(x - -3)

y = -1/4x - 3/4 + 3

y = -1/4 x + 9/4    Multiply through by 4:-

4y = -x + 9    

Karo-lina-s [1.5K]3 years ago
5 0

keeping in mind that perpendicular lines have <u>negative reciprocal</u> slopes, so hmmm wait a second, what is the  slope of 2y=8x−6. anyway?


\bf 2y=8x-6\implies y=\cfrac{8x-6}{2}\implies y=\cfrac{8x}{2}-\cfrac{6}{2}\\\\\\y=\stackrel{\downarrow }{4}x-3\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}


\bf ~\dotfill\\\\\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}}{\stackrel{slope}{4\implies \cfrac{4}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{1}{4}}}


so, we're really looking for the equation of a line whose slope is -1/4 and runs through (-3, 3).


\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})~\hspace{10em}slope = m\implies -\cfrac{1}{4}\\\\\\ \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-3=-\cfrac{1}{4}[x-(-3)]\implies y-3=-\cfrac{1}{4}(x+3)\\\\\\y-3=-\cfrac{1}{4}x-\cfrac{3}{4}\implies y=-\cfrac{1}{4}x-\cfrac{3}{4}+3\implies y=-\cfrac{1}{4}x+\cfrac{9}{4}


now, that equation is fine, is in <u>slope-intercept form</u>, and we can do away with the denominators by simply multiplying both sides by the LCD of all fractions, in this case , 4, and put the equation in <u>standard form</u> instead.


standard form for a linear equation means

- all coefficients must be integers

- only the constant on the right-hand-side

- "x" must not have a negative coefficient


\bf 4(y)=4\left( -\cfrac{1}{4}x+\cfrac{9}{4} \right)\implies 4y=-x+9\implies x+4y=9

You might be interested in
For the arithmetic sequence -3 , -15 , -27 , -39 , -51, ... , The 50th term is .........................
dmitriy555 [2]

Answer:

top leve : nobles

second level:priests

third level: craftment

bottom level:peasent & slavr

3 0
3 years ago
Read 2 more answers
N - 8 = -10<br> Pls find the value of N
xz_007 [3.2K]

Answer:

-2

Step-by-step explanation:

-2 minus 8 equals -10  :)

6 0
3 years ago
Which value is the solution to the open sentence? 2 + 3x= 5
3241004551 [841]

Answer:

x = 1

Step-by-step explanation:

2 + 3*x = 5

3*x = 5 - 2

3*x = 3

x = 3/3

x = 1

3 0
3 years ago
Read 2 more answers
DOES the given value make the inequalities true? x + 9 &gt; 21, when x = 15?
Kobotan [32]

Answer:

Yes.

Step-by-step explanation:

When x=15,

x+9=15+9=24 > 21.

7 0
2 years ago
Read 2 more answers
Someone please help me on both the questions!!!
bonufazy [111]

Step-by-step explanation:

al nth term:

numerator:

=  {n}^{2}

denominator:

= n + 1

so nth term :

=  \frac{ {n}^{2} }{n + 1}

b). 1; 11; 27; 49

first difference: 10; 16; 22

second difference :6

formula for 1st difference:3a+b

formula for 2nd difference:2a

Therefore:

2a=6

a=3

3a+b=10

sub in a

3(3)+b=10

9+b=10

b=1

sub into quadratic formula

{an}^{2}  + bn  + c

(3) {(1)}^{2}  + (1)(1) + c = 1

3(1) + 1 + c = 1

3 + 1 + c = 1

4 + c = 1

c  = - 3

So Tn:

3 {n }^{2}  +  1n - 3

7 0
2 years ago
Read 2 more answers
Other questions:
  • Someone help me please
    7·1 answer
  • The low temperature in one city was -4°F. The low temperature in another city was 8°F. Write an inequality to compare the temper
    9·1 answer
  • Tom bought 20 boxes of flowers. Each box cost him £6. Each box contains 15 flowers. 3/5 He sells of the total number of flowers
    10·2 answers
  • Belkin Co. provides medical care and insurance benefits to its retirees. In the current year, Belkin agrees to contribute 5% of
    8·1 answer
  • 13x - 4 &lt; 12x - 1?................................................
    10·1 answer
  • What shape has 3 equal sides 4 centimeters in length and no right angles
    6·2 answers
  • Can you help just answer by putting
    15·2 answers
  • How am I as a person and a learner of mathematics and science changing my awareness of who mathematicians and scientists are and
    11·1 answer
  • Write from be expressions that are equivalent to 8x + 16.
    11·1 answer
  • What is 9/24 inches?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!