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3 years ago

What is the equation of a line that is parallel to the line with the equation y=2/3x+2 and passes threw the point 1,-1

Mathematics

1 answer:

Lilit [14]3 years ago

5 0

The equation of line parallel to given line is: $y = \frac{2}{3}x-\frac{5}{3}$

Step-by-step explanation:

Given equation of line is:

$y = \frac{2}{3}x+2$

As the line is in slope-intercept form, the co-efficient of x is the slope of the line

So,

$m_1 =\frac{2}{3}$

Let m2 be the slope of required line

As both the lines are parallel,

$m_1 = m_2$

So,

$m_2 = \frac{2}{3}$

The slope intercept form of line is:

$y = mx+b$

Putting the value of the slope

$y = \frac{2}{3}x+b$

To find the value of b, putting (1,-1) in the equation

$-1 = \frac{2}{3}(1) +b\\-1 = \frac{2}{3} +b\\b = -1-\frac{2}{3}\\b = \frac{-3-2}{3}\\b = \frac{-5}{3}$

Putting b=-5/3 in the equation

$y = \frac{2}{3}x-\frac{5}{3}$

Hence,

The equation of line parallel to given line is: $y = \frac{2}{3}x-\frac{5}{3}$

Keywords: Equation of line, slope

Learn more about equation of line at:

#LearnwithBrainly

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a) The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

b) The expected value is 30 and the standard deviation is 5.31.

c) Close to 0% probability that none of the 500 employees has a food allergy

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have food allergy, or they do not. The probability of an adult having allergy is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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This means that $p = 0.06$

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This means that $n = 500$

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The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

(b) What are the expected value and standard deviation of X (i.e., of the population)?

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