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4 years ago

identify an equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1)

Mathematics

2 answers:

Alborosie4 years ago

6 0

Answer:

y-4 = (-1/3)(x+1)

Step-by-step explanation:

We need to identify the equation in point slope form.

The standard equation of point slope form is:

(y-y₁) = m (x-x₁)

where m is the slope and x₁ and y₁ are the points

We are given point(4,-1) so,

x₁=4 and y₁=-1

And a perpendicular line: y =3x+5

Which is equal to y = mx+b

where m is slope so, slope m = 3

Since the line is perpendicular, so the slope in negative inverse of actual slope that m = -1/m

i.e, m = -1/3

So, the equation in point slope form is:

y-(-1) = (-1/3)(x-4)

=> y+1 = (-1/3)(x-4)

Harlamova29_29 [7]4 years ago

3 0

Answer:

The equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓

Step-by-step explanation:

Given

Let P represent the lind

Equation of P; y = 3x + 5

Let Q represent the other point.

Coordinates of Q; Q(4,-1)

It is said that the line P is perpendicular to point Q.

So, the first thing to do is to calculate the slope of Q;

Since both lines are perpendicular, then we make use of formula for calculating the condition of perpendicularity

This is given as m1m2 = -1

Where m1 = slope of P

m2 = slope of Q

To get m1;

m1 is the coefficient of x in equation of line P.

So, m1 = 3.

Now we can solve for m2

m1.m2 = -1. ---- make m2 the subject of formula

m2 = -1/m1

Substitute 3 for m1

m2 = -1/3

m2 = -⅓

Recall that the coordinates of Q is 4 and -1.

To calculate the equation of Q; we make use of the following

m = (y - y1)/(x - x1)

Where m = m2 = -⅓

x1 = 4 and y1 = -1

By substituton, we have

-⅓ = (y - (-1))/(x - 4)

-⅓ = (y + 1)/(x - 4) --- multiply both sides by 3(x - 4)

-⅓ * 3(x - 4) = 3(x - 4) * (y + 1)/(x - 4)

-(x - 4) = 3(y + 1)

-x + 4 = 3y + 3 --- make y the subject of formula

3y = -x + 4 - 3

3y = -x + 1 --- divide through by 3

3y/3 = (-x + 1)/3

y = -x/3 + 1/3

y = -⅓x + ⅓

Hence, the equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓

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a) The 99% confidence interval would be given (0.204;0.296).

b) We have 99% of confidence that the true population proportion of all seafood sold in the country that is mislabeled or misidentified is between (0.204;0.296).

c) No that's not true. Because the necessary assumptions and conditions for the confidence interval for the proportion are satisifed, so then we can use inferential statistics to interpret the interval to the population of interest.

Step-by-step explanation:

Part a

Data given and notation

n=580 represent the random sample taken

X represent the seafood sold in the country that is mislabeled or misidentified by the people

$\hat p=0.25$ estimated proportion of seafood sold in the country that is mislabeled or misidentified by the people

$\alpha=0.01$ represent the significance level (no given, but is assumed)

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A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

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Part c

A government spokesperson claimed that the sample size was too small, relative to the billions of pieces of seafood sold each year, to generalize. Is this criticism valid?

No that's not true. Because the necessary assumptions and conditions for the confidence interval for the proportion are satisifed, so then we can use inferential statistics to interpret the interval to the population of interest.

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