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
What is the greatest common divisor of 33489, 3948, and 3949
storchak [24]

33489 = 32×612

3948 = 22×3×7×47

3949 = 11×359

GCD = 1

33489 / 1 = 33489

3948 / 1 = 3948

3949 / 1 = 3949

3 0
3 years ago
How many times larger is 4 × 10^10 than 2 × 10^8?
fgiga [73]

Answer:10

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The teacher paid $12 for 6 pounds of candy. Which statement is true about her unit<br> rate?
Hunter-Best [27]

Answer:

For every pound of candy, the teacher spent $2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
While cleaning, Tim discovers eighteen decks of standard playing cards (each deck has 52-cards composed of 13 hearts, clubs, dia
Sidana [21]

Answer:

multiply all off that and get your andser

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=Solve%3A%202x%20%2B%207%20%3D%20-11PLS%20HELP%20ILL%20GIVE%20YOU%20BRAINLIEST" id="TexFormula1
Lena [83]

Answer:

-9

Step-by-step explanation:

2x + 7 = -11

2x = -11 - 7

2x = -18

x = -9

7 0
3 years ago
Other questions:
  • A pile of sand has a weight of 90kg the sand is put into a small bag and a medium bag and a large bag in the ratio 2:3:7
    15·1 answer
  • Solve the equation: log4(x + 20) = 3
    15·2 answers
  • Kathleen had a bag of candy-coated chocolates. Of the 55 candies in the bag, 20% were red, 30% were orange, 30% were green, and
    15·2 answers
  • Let x represent each number. write an equation and solve for the variable.
    7·1 answer
  • What is 8756 x 6734 I need this for homework please help me
    11·1 answer
  • Any Simple way to learn mathematics formula ?​
    8·2 answers
  • The following are the ages (years) of 5 people in a room:
    6·1 answer
  • Marks books has an area of 48 in.². The perimeter of the book is 52 inches. what are the dimensions of the book
    6·1 answer
  • An antique chair was purchased in the year 2013 for $500. At the time of purchase, an appraiser estimated that
    14·1 answer
  • What is the answer please?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!