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3 years ago

12

What is the equation of a line with a slope of -4 that passes through the point (1,2)

2 answers:

laila [671]3 years ago

8 0

Answer: Write an equation of the line that passes through the point (1,2) and has the slope, m = 2. I'm very bad at Math so please answer this question! I need all the help I can get. Thank you so much!

Step-by-step explanation:

Anika [276]3 years ago

5 0

Answer:

y = -4x + 6

Step-by-step explanation:

The easiest-to-use form of the equation of a straight line is y = mx + b.

Substitute -4 for m, 1 for x and 2 for y, to obtain the y-intercept, b:

2 = -4(1) + b, so b = 6, and y = -4x + 6

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Alecsey [184]

Answer:

The function is $P(x) = \frac{1}{2} e^{-x^2} +0.016$

Step-by-step explanation:

From the question we are told that

The rate of growth is $P'(x) = xe^{x} - x^2$

The total profit is $P(2) =$ $25,000

The time taken to make the profit is $x = 2 \ years$

From the question

$P'(x) = xe^{-x^2}$ is the rate of growth

Now here x represent the time taken

Now the total profit is mathematically represented as

$P(x) = \int\limits {P'(x)} \, = \int\limits {xe^{-x^2}} \,$

So using substitution method

We have that

$u = - x^2$

$du = 2xdx$

So

$p(x) = \int\limits {\frac{1}{2} e^{-u}} \, du$

$p(x) = {\frac{1}{2} [ e^{-u}} +c ]$

$p(x) = {\frac{1}{2} e^{-x^2}} + \frac{1}{2} c$ recall $u = - x^2$ and let $\frac{1}{2} c = Z$

At x = 2 years

$P(x) =$ $25,000

So

Since the profit rate is in million

$P(x) =$ $25,000 = $\frac{25000}{1000000} =$ $0.025 millon dollars

So

$0.025 = {\frac{1}{2} e^{-2^2}} + Z$

=> $Z = 0.025 - {\frac{1}{2} e^{-2^2}}$

$Z = 0.016$

So the profit function becomes

$P(x) = \frac{1}{2} e^{-x^2} +0.016$

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