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
Mkey [24]
3 years ago
10

Graph each linear equation that passes through the given pair of points. Use graph paper.

Mathematics
1 answer:
Naya [18.7K]3 years ago
6 0

Answer:

The easier way to solve this is to find the two points in the coordinate axis, and just draw a line that passes through the two points.

But let's be more complete:

Let's find the equations for each line:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

1) Here the points are (2,2) and (4,5)

then the slope is:

a = (5 - 2)/(4 - 2) = 3/2

y = (3/2)*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (2, 2)

2 = (3/2)*2 + b

2 = 3 + b

2 - 3 = b

-1 = b

y = (3/2)*x - 1

2) Here the points are (0,1/2) and (2,3/2)

then the slope is:

a = (3/2 - 1/2)/(2 - 0) = 1/2

y = (1/2)*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (0, 1/2)

1/2 = (1/2)*0 + b

1/2 = b

y = (1/2)*x + 1/2

3) Here the points are (-1,2) and (5,0)

then the slope is:

a = (0 - 2)/(5 + 1) = -1/3

y = (-1/3)*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-1, 2)

2 = (-1/3)*-1 + b

2 = 1/3 + b

2 - 1/3 = b

5/3 = b

y = (-1/3)*x + 5/3

4) Here the points are (-5,-3) and (-3,5)

then the slope is:

a = (5 + 3)/(-3 + 5) = -4

y = -4*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-3, 5)

5 = -4*-3 + b

5 = 12 + b

5 - 12 = b

-7 = b

y = -4*x - 7

Now that we have all the equations, we can find the graphs.

where the colors are:

(4) green

(3) orange

(2) Blue

(1) Gray.

You might be interested in
Please help me I’m really stuck
dalvyx [7]

Answer:

<u>/</u><u> </u>3=<u>/</u><u> </u>5 { alternate anglea}

<u>/</u><u> </u>5+<u>/</u>6 =180° {straight angle}

<u>/</u><u> </u>6=180-26

<u>/</u><u> </u>6=154°

hope it helps

<h3>stay safe healthy and happy.</h3>
6 0
3 years ago
In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank
fredd [130]

Answer:

1) Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) Amount \ of \, water \ remaining \ in \, the \ tank \ is \  \frac{x^3(6-\pi) }{6}

Step-by-step explanation:

1) Here we have;

First tank A

Volume of tank = x³

The  volume of the sphere = \frac{4}{3} \pi r^3

However, the diameter of the sphere = x therefore;

r = x/2 and the volume of the sphere is thus;

volume of the sphere = \frac{4}{3} \pi \frac{x^3}{8}= \frac{1}{6} \pi x^3

For tank B

Volume of tank = x³

The  volume of the spheres = 8 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 2·D = x therefore;

r = x/4 and the volume of the sphere is thus;

volume of the spheres = 8 \times \frac{4}{3} \pi (\frac{x}{4})^3= \frac{x^3 \times \pi }{6}

For tank C

Volume of tank = x³

The  volume of the spheres = 64 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 4·D = x therefore;

r = x/8 and the volume of the sphere is thus;

volume of the spheres = 64 \times \frac{4}{3} \pi (\frac{x}{8})^3= \frac{x^3 \times \pi }{6}

Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) For the 4th tank, we have;

number of spheres on side of the tank, n is given thus;

n³ = 512

∴ n = ∛512 = 8

Hence we have;

Volume of tank = x³

The  volume of the spheres = 512 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 8·D = x therefore;

r = x/16 and the volume of the sphere is thus;

volume of the spheres = 512\times \frac{4}{3} \pi (\frac{x}{16})^3= \frac{x^3 \times \pi }{6}

Amount of water remaining in the tank is given by the following expression;

Amount of water remaining in the tank = Volume of tank - volume of spheres

Amount of water remaining in the tank = x^3 - \frac{x^3 \times \pi }{6} = \frac{x^3(6-\pi) }{6}

Amount \ of \ water \, remaining \, in \, the \ tank =  \frac{x^3(6-\pi) }{6}.

5 0
3 years ago
Need help with this! Due in 10 mins please
svetlana [45]
True for some cases
7 0
3 years ago
Read 2 more answers
Find equation to this line​
kondor19780726 [428]

Answer:

the equation of this line is y= 1x+6

8 0
3 years ago
Mentally solve 18 × 25
koban [17]

Answer:

450

Step-by-step explanation:

Step 1:

18 × 25 = 450

Answer:

450

Hope This Helps :)

3 0
3 years ago
Read 2 more answers
Other questions:
  • The moon is about 240,000 miles from earth what is the order of magnitude of this number
    10·2 answers
  • What is the product of (2p+7)(3p^2 +4p-3)
    6·1 answer
  • Does anyone know the answer please help!!
    11·1 answer
  • 1. Emmanuel bought 28 lb of potting soil this week. This amount is 4 lb more than twice the amount of potting soil he bought las
    13·1 answer
  • Avery uses a blend of dark chocolate and milk chocolate to make the ice cream topping at her restaurant. She wants to buy 10 kg
    9·1 answer
  • a small plane lands at a point 324 miles east and 92 miles north of the point at which it took off. Find the distance the plane
    10·1 answer
  • I will give you Brainiest if you are right.
    6·2 answers
  • What about linear equations
    7·1 answer
  • 3(3u-2)=2(3u+3)<br> What is the steps
    11·1 answer
  • What can u round 5,201
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!