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2 years ago

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⦁ Write an equation of a line in slope intercept form (y = mx + b) with slope 1/3 going through the point (-6, 2). Show your wor

k for full credit.

1 answer:

Zepler [3.9K]2 years ago

3 0

$(\stackrel{x_1}{-6}~,~\stackrel{y_1}{2})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \\\\\\ y-2=\cfrac{1}{3}(x+6)\implies y-2=\cfrac{1}{3}x+2\implies y=\cfrac{1}{3}x+4$

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Answer:

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Step-by-step explanation:

The first one is equal to x-4

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3 years ago

Which equation could you use to find 15 ÷ 3? 15 + 3 = 18 18 – 3 = 15 3 × 5 = 15 30 ÷ 2 = 15

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3 years ago

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3 years ago

Read 2 more answers

Find the angle that the line through the given pair of points makes with the positive direction of the x-axis

alexdok [17]

Answer:

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

Step-by-step explanation:

Given:

Let

A(x₁ , y₁) = (1 , 4) and

B( x₂ , y₂ ) = (-1 , 2)

To Find:

θ = ?

Solution:

Slope of a line when two points are given is given bt

$Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Substituting the values we get

$Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1$

Also Slope of line when angle ' θ ' is given as

$Slope=\tan \theta$

Substituting Slope = 1 we get

$1=\tan \theta$

$\tan \theta=1\\\theta=\tan^{-1}(1)$

We Know That for angle 45°,

tan 45 = 1

Therefore

$\theta=45\°$

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

5 0

3 years ago

The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by about 7.2% per year. Write an expo

xeze [42]

<h2>Hello!</h2>

The answer is:

In 2036 there will be a population of 32309 rabbits.

<h2>Why?</h2>

We can calculate the exponential decay using the following function:

$P(t)=StartAmount*(1-\frac{percent}{100})^{t}$

Where,

Start Amount, is the starting value or amount.

Percent, is the decay rate.

t, is the time elapsed.

We are given:

$StartAmount=144,000\\x=7.2(percent)\\t=2036-2016=20years$

Now, substituting it into the equation, we have:

$P(t)=StartAmount(1-\frac{percent}{100})^{t}$

$P(t)=144000*(1-\frac{7.2}{100})^{20}$

$P(t)=144000*(1-0.072)^{20}$

$P(t)=144000*(0.928)^{20}$

$P(t)=144000*(0.928)^{20}$

$P(t)=144000*0.861=32308.888=32309$

Hence, we have that in 2036 the population of rabbis will be 32309 rabbits.

Have a nice day!

5 0

3 years ago