3 years ago

Which are the responsibility of the government? Check all that apply.

1 answer:

3 0

Governments are responsible for providing services that individuals cannot effectively provide for themselves, such as military defense, fire and police departments, roads, education, social services, and environmental protection.

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Write the equation of the line that goes through the point (−9, −4) and is parallel to the line −x + 3y = −0.5

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Answer:

$y = \frac{1}{3}x -1$

Explanation:

Given

Parallel to: $-x + 3y = -0.5$

Passes through (-9,-4)

Required

Determine the line equation

First, we calculate the slope (m) of the said line

$-x + 3y = -0.5$

Make y the subject

$3y = x - 0.5$

Divide through by 3

$y = \frac{1}{3}x - \frac{0.5}{3}$

An equation has the general form:

$y = mx + b$

Where

$m = slope$

So:

$m = \frac{1}{3}$

Because the required line is parallel to $-x + 3y = -0.5$ , then they have the same slope of $m = \frac{1}{3}$

Next, is to calculate the line equation using:

$y = m(x - x_1) + y_1$

Where

$m = \frac{1}{3}$

$(x_1,y_1) = (-9,-4)$

This gives:

$y = \frac{1}{3}(x -(-9)) + (-4)$

$y = \frac{1}{3}(x +9) -4$

Open bracket

$y = \frac{1}{3}x +3 -4$

$y = \frac{1}{3}x -1$

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