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
anzhelika [568]
3 years ago
13

Carlota wrote the equation y + 1 = 2 (x - 3) for the line passing through the points (-1, 3) and (2, 9). Explain and correct her

error.
Mathematics
1 answer:
Art [367]3 years ago
5 0

For this case we have the following equation:


y + 1 = 2 (x - 3)

That can be rewritten in the form y = mx + b

Where:


  • m is the slope of the line
  • b is the cut point

So, we have:


y + 1 = 2 (x - 3)\\y + 1 = 2x-6\\y = 2x-6-1\\y = 2x-7

Where:


m = 2 is the slope


b = -7 is the cut point


Carlota has the following points:


(-1, 3) and (2, 9)


To know if the line y = 2x-7 passes through these points, we must replace them in the equation and the equality must be fulfilled. So:


Point (-1, 3):


Substituting:


3 = 2 (-1) -7\\3 = -2-7

3 = -9 It's false, equality is not met. The point (-1, 3) does not go through the line.


The equation written by Carlota is erroneous, the procedure to follow is:


Given(x1, y1) = (- 1, 3) and(x2, y2) = (2, 9), we find the slope:


m=\frac{(y2-y1)}{(x2-x1)}

m=\frac{(9-3)}{(2-(-1))}

m=\frac{6}{3}

m=2

We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:


y = 2x + b

Substituting (2,9) we have:


9 = 2 (2) + b\\9 = 4 + b\\b = 9-4\\b = 5

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is y = 2x + 5

Answer:


The correct equation of the line that passes through the given points is y = 2x + 5

Carlota's mistake was at the cutoff point


You might be interested in
You run one lap around a mile track every 8 minutes. Your friend runs around the same track every 10 minutes. You both start at
Ber [7]

Answer:

Step-by-step explanation:

first runs n+1 laps

and second runs n laps in the same time.

so (n+1)8=10n

10n=8n+8

10n-8n=8

2n=8

n=8/2=4

one lap=1 mile

4 laps=4 miles

4+1=5 laps=5 miles.

first runs 5 miles whereas second runs=4 miles.

3 0
3 years ago
Read 2 more answers
If a is an integer, prove that (14a + 3, 21a + 4) = 1.
Firdavs [7]

Answer:

(14a+3, 21+4) = 1

Step-by-step explanation:

We are going to use the Euclidean Algorithm to prove that these two integers have a gcd of 1.

gcd (14a + 3, 21a + 4) = gcd (14a+3, 7a + 1) = gcd (1, 7a+1) = 1

Therefore,

(14a + 3, 21a + 4) = 1

8 0
3 years ago
What is the slope of the equation y = 3x + 2?
Softa [21]

Answer:

3

Step-by-step explanation:

the equation is y=mx+b

m=slope

so then 3 would be the slope

hope this helps :3

if it did pls mark brainliest

7 0
3 years ago
Read 2 more answers
Plz help me i did it but messed up some ware plz help . 5x5=4x5+9=
Lyrx [107]

Answer: 25=29

Step-by-step explanation:5x5=25

4x5+9=29

5 0
3 years ago
Read 2 more answers
N = {X:X<br>is an odd number, 21&lt;x&lt;3<br>XEN]​
SIZIF [17.4K]
So it’s saying that the following set in roster form: (1) N = (x :x is an odd number, 21< × ≤ 35,×€ N)?

It seems to be that the Roster form would do not do anything but the thing is that this listing would give us the output of a set from this problem.

Your answer would be, N = Set of Odd Numbers such that x is greater than 21 and less than or equal to 35 = {23, 25, 27, 29, 31, 33, 35}.
5 0
3 years ago
Other questions:
  • A collection of dimes and nickels is worth $8.40 there are 106 coins how many of each are there
    5·1 answer
  • What is the correct multiplication of a cross product to solve for the missing dimension?
    10·3 answers
  • Describe any pattern you see in this sequence of ordered pairs: (1,1800), (2,900), (3,300), (4,100)
    11·1 answer
  • I need to know if the answer to number 9. Is correct
    13·1 answer
  • Which equation can be used to solve for the unknown number? Seven less than a number is thirteen.
    14·2 answers
  • Mr.marichal has quarters ,dimes,and pennies in a jar.he has twice as many quarters as oennies.he also has 5 more dimes than penn
    15·1 answer
  • Simplify the radical expression.
    7·1 answer
  • Here are the ingredients needed to make 20 cookies.
    7·1 answer
  • Write a trinomial whose binomial factors contain constant terms that sum to −11 and have a product of 18.
    12·1 answer
  • EASY MATH ALGEBRA 1 PLEASE HELP FAST GIVING BRAINLIEST IF CORRECT!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!