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mylen [45]
3 years ago
15

Each line represents a proportional relationship. Write an equation for each line. Show your work.

Mathematics
1 answer:
tiny-mole [99]3 years ago
7 0

Answer:

The equation of line a is y = x

The equation of line b is y =  \frac{2}{3} x

Step-by-step explanation:

The equation of the proportional is y = m x, where

  • m is the slope of the line (constant of proportionality)

The rule of the slope of a line is m = \frac{y2-y1}{x2-x1} , where

  • (x1, y1) and (x2, y2) are two points on the line

∵ Line a passes through points (0, 0) and (3, 3)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = \frac{3-0}{3-0}=\frac{3}{3}

∴ m = 1

→ Substitute in the form of the equation above

∴ y = (1)x

∴ y = x

∴ The equation of line a is y = x

∵ Line b passes through points (0, 0) and (3, 2)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 2

→ Substitute them in the rule of the slope above

∵ m = \frac{2-0}{3-0}=\frac{2}{3}

∴ m = \frac{2}{3}

→ Substitute in the form of the equation above

∴ y = (\frac{2}{3}) x

∴ y =  \frac{2}{3} x

∴ The equation of line b is y =  \frac{2}{3} x

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Using your answer from part (b) and inequality symbols, write one statement that shows the relationship among all of the numbers
Natali5045456 [20]

Answer:

(b) Least to greatest numbers are -1.0, -\frac{1}{4} , 0, 0.5, 1.5

(c) -1.0 <  -\frac{1}{4}  < 0 < 0.5 < 1.5

OR

1.5 > 0.5 > 0 >  -\frac{1}{4}  > -1.0

Step-by-step explanation:

P.S - The exact question is -

Given - Kendra collected data for her science project. She surveyed

             people asking them how many hours they sleep during a

             typical night.

             The chart below shows how each person’s response compares

              to 8 hours (which is the answer she  expected most people to say).

Name                Number of Hours                       Compared to Hours

                         (usually slept each night)

Frankie                        8.5                                                    0.5

Mr. Fields                      7                                                      −1.0

Karla                             9.5                                                     1.5

Louis                             8                                                         0

Tiffany                            7\frac{3}{4}                                                       -\frac{1}{4}

To find - (a) Plot and label each of the numbers in the right-most column

                   of the table above on the number line below.

               (b) List the numbers from least to greatest.

                (c) Using your answer from part (b) and inequality symbols,

                     write one statement that shows the relationship  among all

                     of the numbers.

Proof -

(a)

We can see that the numbers in the right-most column are  0.5, -1.0, 1.5, 0, -\frac{1}{4}

We can write -\frac{1}{4} = -0.25

Now,

We have to label them in the number line

The number line is as follows :

(b)

Least to greatest numbers are -1.0, -\frac{1}{4} , 0, 0.5, 1.5

(c)

By using inequality symbol, we get

-1.0 <  -\frac{1}{4}  < 0 < 0.5 < 1.5

OR

1.5 > 0.5 > 0 >  -\frac{1}{4}  > -1.0

5 0
3 years ago
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ale4655 [162]

Answer:

-1 < x < 4.

Step-by-step explanation:

- 6 < 2x - 4 <4

2x - 4 < 4

2x < 8

x < 4.    Also we have:

2x - 4 > -6

2x > -2

x > -1.

5 0
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Nataliya [291]

Step-by-step explanation:

For the quadratic equation to have 1 repeated real solution, the discriminant b² - 4ac must be zero.

=> (-z)² - 4(z - 5)(5) = 0

=> z² - 20(z - 5) = 0

=> z² - 20z + 100 = 0

=> (z - 10)² = 0

Therefore z = 10.

7 0
3 years ago
12 inches increased by 36
crimeas [40]
12 + 36 = 48

your answer is 48 inch

hope this helps
7 0
3 years ago
Read 2 more answers
Determine the value of cos 79º 15' (cosine of 79 degrees, and 15 minutes). In this case, minutes are 1/60 of a degree.
yKpoI14uk [10]

Answer:

A. 0.186524036

Step-by-step explanation:

Cosine 79° 15'

But, 1° = 60'

Thus; 15' = 15/60 = 0.25°

Therefore;

cos 79° 15' = cos 79.25°

Cos 79.25° = 0.186524036

                  = 0.186524036

8 0
3 years ago
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