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natima [27]
2 years ago
8

Write the equation of the line that passes through the points (2, 1) and (5, -8)

Mathematics
1 answer:
My name is Ann [436]2 years ago
4 0

Answer:

The answer is y = -3x + 7.

Step-by-step explanation:

❃Incase you forgot what the linear equation formula is ☟

y = mx + b

❃Incase you also forgot, what the slope formula is ☟

m =  \frac{y_2 - y_1}{x_2 - x_1}

➊ First: We are going to be solving for the slope.

m =  \frac{ - 8 - 1}{5 - 2}  =  \frac{ - 9}{ \:  \:  \: 3}  =  - 3

➋Second: We find the y-intercept.

y = mx + b \\ 1 = - 3(2) + b \\ 1 = - 6 + b \\ \frac{ + 6 = + 6 \: \: \: \: \:  \:  \:  \:  \: }{7 = b}

➌Third: Plug in.

y =  - 3x + 7

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Answer:

2

Step-by-step explanation:

f(-1)=2(-1)+2+1

f(-1)=-2+2+1

f(-1)=1

f(0)=2(0)+2+1

f(0)=0+2+1

f(0)=3

Use slope formula for the average rate of change.

(y2-y1)/(x2-x1)

(3-1)/(0+1)

(2)/(1)

2

Hope this helps!

If not, I am sorry.

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2 years ago
Natasha ran 3.1 kilometers. Tonya ran 4 meters more than half as far as Natasha. How many meters did Tonya run?
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4 0
3 years ago
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat
NeTakaya

Answer:

The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

    35x = -0.05(x² - 800x + 160000) + 9492

    35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

    35x = -0.05x² +40x - 8000 + 9492

    35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

0.05x² - 5x -1492 = 0

Using the quadratic formula,

x = \frac{-(-5) +/- \sqrt{(-5)^{2} - 4 X 0.05 X - 1492}  }{2X0.05}   = \frac{5 +/- \sqrt{25 + 298.4}  }{0.1} =  \frac{5 +/- \sqrt{323.4}  }{0.1}\\=  \frac{5 +/- 17.983 }{0.1}\\=  \frac{5 - 17.983 }{0.1}  or  \frac{5 + 17.983 }{0.1}\\= \frac{-12.983 }{0.1} or  \frac{22.983 }{0.1}\\= -129.83 or 229.83

We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.

The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1

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3 years ago
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AleksandrR [38]

592 \div 2 = 296 - 58 = 238
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3 years ago
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