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
makkiz [27]
3 years ago
11

Write an equation in standard form for the line that passes through the point (2,-3) and is perpendicular to the line y + 4 = -2

/3(x-12)
Mathematics
1 answer:
sineoko [7]3 years ago
5 0

For this case we have that by definition, the standard form of a linear equation is given by:

ax + by = c

By definition, if two lines are perpendicular then the product of their slopes is -1. That is to say:

m_ {1} * m_ {2} = - 1

We have the following point-slope equation of a line:

y+4 = -\frac {2} {3}(x-12)

The slope is:

m_ {1} = - \frac {2} {3}

We find the slope m_ {2}of a perpendicular line:

m_ {2} = \frac {-1}{m_ {1}}\\m_ {2} = \frac {-1} {-\frac {2} {3}}\\m_ {2} = \frac{3} {2}

Thus, the equation is of the form:

y-y_ {0} = \frac {3} {2} (x-x_ {0})

We have the point through which the line passes:

(x_ {0}, y_ {0}) :( 2, -3)

Thus, the equation is:

y - (- 3) = \frac {3} {2} (x-2)\\y + 3 = \frac {3} {2} (x-2)

We manipulate algebraically:

y + 3 = \frac{3} {2} x- \frac {3} {2} (2)\\y + 3 = \frac{3} {2} x-3

We add 3 to both sides of the equation:

y + 3 + 3 = \frac {3} {2} x\\y + 6 = \frac {3} {2} x

We multiply by 2 on both sides of the equation:

2(y + 6) = 3x\\2y + 12 = 3x

We subtract 3x on both sides:

2y-3x + 12 = 0

We subtract 12 from both sides:

2y-3x = -12

ANswer:

-3x + 2y = -12

You might be interested in
The length of a rectangle is 4 units less than the width. The area of the rectangle is 21 units. What is the length, in units, o
bazaltina [42]

The formula of an area of a rectangle:

A = wl

We have l = w - 4 and A = 21.

Substitute:

w(w - 4) = 21       <em>use distributive property</em>

(w)(w) + (w)(-4) = 21

w² - 4w = 21     <em>subtract 21 from both sides</em>

w² - 4w - 21 = 0

w² - 7w + 3w - 21 = 0

w(w - 7) + 3(w - 7) = 0

(w - 7)(w + 3) = 0 ↔ w - 7 = 0 ∨ w + 3 = 0

w = 7 ∨ w = -3 < 0

l = w - 4 → l = 7 - 4 = 3

<h3>Answer: the length = 3 u.</h3>
4 0
3 years ago
Use the info given to find the new price: original price: $24 and discount rate: 11%. What is the new price????
ELEN [110]
So I think you have to find 11% of 24 and that is 11/100 x 24 = 2.64$. Then you reduce it to the real price 24-2.64= 21.36$ (the new prize). I might be completly wrong but I hope this helps
3 0
3 years ago
Plz plz help test due soon
Dvinal [7]

Answer:

22

Step-by-step explanation:

8 0
3 years ago
What is a synonym for diseases
polet [3.4K]
Uhm disorder, condition, illness ? 
6 0
3 years ago
Read 2 more answers
An equivalent expression to a2/3
scoundrel [369]

Answer:

4/6  6/9  8/12  10/15 and so on, just multiply both the numerator and denominator by the same number and get your answer.

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • What is 4/3 times 9/16
    14·1 answer
  • Answer this question please
    7·1 answer
  • What is the length of the unknown
    6·1 answer
  • How many ones can you take from seventeen
    8·1 answer
  • Find the area of a circle with a diameter of 6.
    10·1 answer
  • A family has two children. If the genders of these children are listed in the order they are born, there are four possible outco
    10·1 answer
  • What is the square root of 37
    8·1 answer
  • Anja buys a magazine and a pizza. She spends $9.75. The pizza costs twice the amount of the magazine. How much does the pizza co
    8·1 answer
  • Please help i will give you 100 points
    15·2 answers
  • 0.00002165 in scientific notation.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!