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
jok3333 [9.3K]
2 years ago
7

Determine whether the lines given in each box are parallel, perpendicular, or neither

Mathematics
1 answer:
andrey2020 [161]2 years ago
5 0

Answer/Step-by-sep explanation:

To determine whether the lines given in each box are parallel, perpendicular, or neither, take the following simple steps:

1. Ensure the equations for both lines being compared are in the slope-intercept form, y = mx + b. Where m is the slope.

2. If both lines have the same slope value, m, then both lines are parallel.

3. If the slope of one line is the negative reciprocal of the other, then both lines are perpendicular. That is, x = -1/x.

4. If the slope of both lines are not the same, nor the negative reciprocal of each other, then they are neither parallel nor perpendicular.

1. y = 3x - 7 and y = 3x + 1.

Both have the same slope value of 3. Therefore, they are parallel.

2. ⬜ y = -\frac{2}{5}x + 3 and y = \frac{2}{5}x + 8

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -⅖ and the slope of the other is ⅖. Therefore, they are neither parallel nor perpendicular.⬜

3. y = -\frac{1}{4}x and y = 4x - 5

The slope of the first line, ¼, is the negative reciprocal of the slope of the second line, 4.

Therefore, they are perdendicular.

4. 2x + 7y = 28 and 7x - 2y = 4.

Rewrite both equations in the slope-intercept form, y = mx + b.

2x + 7y = 28

7y = -2x + 28

y = -2x/7 + 28/7

y = -²/7 + 4

And

7x - 2y = 4

-2y = -7x + 4

y = -7x/-2 + 4/-2

y = ⁷/2x - 2

The slope of the first line, -²/7, is the negative reciprocal of the slope of the second line, ⁷/2.

Therefore, they are perdendicular.

5.⬜ y = -5x + 1 and x - 5y = 30.

Rewrite the second line equation in the slope-intercept form.

x - 5y = 30

-5y = -x + 30

y = -2x/-5 + 30/-5

y = ⅖x - 6

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -5 and the slope of the other is ⅖. therefore, they are neither parallel nor perpendicular.⬜

6.⬜ 3x + 2y = 8 and 2x + 3y = -12.

Rewrite both line equations in the slope-intercept form.

3x + 2y = 8

2y = -3x + 8

y = -3x/2 + 8/2

y = -³/2x + 4

And

2x + 3y = -12

3y = -2x -12

y = -2x/3 - 12/3

y = -⅔x - 4

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -³/2 and the slope of the other is -⅔ therefore, they are neither parallel nor perpendicular.⬜

7. y = -4x - 1 and 8x + 2y = 14.

Rewrite the equation of the second line in the slope-intercept form.

8x + 2y = 14

2y = -8x + 14

y = -8x/2 + 14/2

y = -4x + 7

Both have the same slope value of -4. Therefore, they are parallel.

8.⬜ x + y = 7 and x - y = 9.

Rewrite the equation of both lines in the slope-intercept form.

x + y = 7

y = -x + 7

And

x - y = 9

-y = -x + 9

y = -x/-1 + 9/-1

y = x - 9

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -1, and the slope of the other is 1, therefore, they are neither parallel nor perpendicular.⬜

9. y = ⅓x + 9 And x - 3y = 3

Rewrite the equation of the second line.

x - 3y = 3

-3y = -x + 3

y = -x/-3 + 3/-3

y = ⅓x - 1

Both have the same slope value of ⅓. Therefore, they are parallel.

10.⬜ 4x + 9y = 18 and y = 4x + 9

Rewrite the equation of the first line.

4x + 9y = 18

9y = -4x + 18

y = -4x/9 + 18/9

y = -⁴/9x + 2

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -⁴/9, and the slope of the other is 4, therefore, they are neither parallel nor perpendicular.⬜

11.⬜ 5x - 10y = 20 and y = -2x + 6

Rewrite the equation of the first line.

5x - 10y = 20

-10y = -5x + 20

y = -5x/-10 + 20/-10

y = ²/5x - 2

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is ⅖, and the slope of the other is -2, therefore, they are neither parallel nor perpendicular.⬜

12. -9x + 12y = 24 and y = ¾x - 5

Rewrite the equation of the first line.

-9x + 12y = 24

12y = 9x + 24

y = 9x/12 + 24/12

y = ¾x + 2

Both have the same slope value of ¾. Therefore, they are parallel.

You might be interested in
Find the 8th term in the sequence with this explicit formula:<br> c(n) = -6 + 5(n - 1)
QveST [7]

We are given this explicit formula :

c(n) = -6 + 5(n - 1)

In order to find eighth term let us plug n as 8 in this formula:

c(8) = -6 + 5(8 - 1)

subtracting 8-1 first using pemdas rule

c(8) = -6 + 5(7)

multiplying 5 and 7

c(8) = -6 + 35

subtracting 35-6

c(8) = 29

So eighth term is 29.

6 0
3 years ago
BRAINLIEST PLEASSEEEEE HELP
vladimir1956 [14]

Pick the second one I did the math on it

4 0
2 years ago
A company claims its washing machine produces 4000 joules of work output for every 3000 joules of work input. What would make yo
ycow [4]

Things that make me skeptical: No evidence is provided, the company also claims that its washing machine produces 4000 joules of output for ever 3000 joules of input, and there is no possible way of creating a joule output larger than the input, unless your using coils to increase electricity, but that's not what washing machines have inside of their machinery. Washing machines don't have mini Tesla coils inside their machinery!

I hope this helps!

5 0
3 years ago
josiah is ready to purchase a new watch. it is regularly priced at $480.77. the sale price is $380.54. what is the mark down on
dem82 [27]
20.8478066 (or 20.85%)
you do 480.77 minus 380.54 and it comes out to 100.23 and then you do 100.23/480=x/100 (discount/original=percent/100) and you multiply 100.23 by 100 and it comes to 10023 and you do 10023 divided by 480.77 and it comes out to 20.8478066 or 20.85%
6 0
3 years ago
Rectangles ABCD and EFGH are similar. The perimeter of rectangle ABCD is 5 times greater than the perimeter of rectangle EFGH. W
yulyashka [42]
C.  Area of rectangle is A=L X W

If the length is 5 times bigger and the width is 5 times bigger, than the area is 25 times bigger
7 0
3 years ago
Read 2 more answers
Other questions:
  • In the diagram below ab is parallel to cd what is the value of x
    7·2 answers
  • a chemistry lab, you have 2 vinegars. One is 5% acetic acid, and the other one is 6% acetic acid. You want to make 200 ml of vin
    13·1 answer
  • At a basketball​ game, a team made 57 successful shots. They were a combination of​ 1- and​ 2-point shots. The team scored 99 po
    13·1 answer
  • What is the perimeter of the room?<br>5 yd<br>. What is the area of the room?<br>4 yd​
    9·1 answer
  • Cody's Cafe uses 1 7/10 bags of coffee every day. How many days will 6 4/5 bags of coffee last?
    11·1 answer
  • Please help I will give brainliest!!
    9·1 answer
  • Please help don’t play around it’s important
    9·2 answers
  • Help pls !!!!!!!brainliest goes to first right answer
    13·1 answer
  • Please help me with these questions :(
    11·1 answer
  • Hanna and Dien are both getting a raise. Who will earn more<br> per hour after the raise?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!