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BARSIC [14]
2 years ago
8

The equation of a line is y = 2x + 3. What is the equation of the line that is parallel to the first line and passes through (2,

–1)?
Mathematics
1 answer:
Masja [62]2 years ago
8 0

Answer:

y = 2x - 5

Step-by-step explanation:

The slope for a parallel line is the same as the slope in the given equation.  Therefore the slope of the new line will be 2    m= 2

use that slope and (2, -1) to find b

-1 = 2(2) + b

-1 = 4 + b

-5 = b

Plug m and b into y = mx + b

y = 2x - 5

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2 years ago
Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different
N76 [4]

Answer:

(a)  As time increases, the amount of water in the pool increases.

     11 gallons per minute

(b)  65 gallons

Step-by-step explanation:

From inspection of the table, we can see that <u>as time increases, the amount of water in the pool increases</u>.

We are told that Ann adds water at a constant rate.  Therefore, this can be modeled as a linear function.  

The rate at which the water is increasing is the <em>rate of change</em> (which is also the <em>slope </em>of a linear function).

Choose 2 ordered pairs from the table:

\textsf{let}\:(x_1,y_1)=(8, 153)

\textsf{let}\:(x_2,y_2)=(12,197)

Input these into the slope formula:

\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11

Therefore, the rate at which the water in the pool is increasing is:

<u>11 gallons per minute</u>

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

y-y_1=m(x-x_1)

\implies y-153=11(x-8)

\implies y-153=11x-88

\implies y=11x-88+153

\implies y=11x+65

When Ann had added no water, x = 0.  Therefore,

y=11(0)+65

y=65

So there was <u>65 gallons</u> of water in the pool before Ann starting adding water.

3 0
2 years ago
Read 2 more answers
Solve for x. 15x + 6 = 10x + 21 x = -5 x = 5 x = 3 x = 5
klio [65]
Move all the x terms to one side and solve for x. 15x-10x=21-6 : 5x/5=15/5 : x=3
4 0
3 years ago
What do symbols represent in algebra?
Inessa05 [86]

Answer:

One of the most common algebraic symbols is the use of x, y or another letter of the alphabet to indicate a variable or unknown quantity. Common symbols used in algebra also include those related to equality, inequality, factorials and organization, like braces, brackets and parentheses.

Give brainiest please ;-;

7 0
2 years ago
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A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function
yan [13]
For this case we have the following equation:
 h = -16t2 + 32t + 6
 Deriving we have:
 h '= -32t + 32
 Equaling to zero:
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 We clear the time:
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 Answer:
 
The ball reaches its maximum height in:
 
t = 1 s
 
The ball's maximum height is:
 
h (1) = 22 feet
 
option: 22 ft, 1 s
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3 years ago
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