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Hello i have some questions i do not understand.

1. To the nearest tenth, what is the distance in units between the points (-2, 5) and (4,1)?

2. Which of the following shows a direct proportional relationship?
y =4x
y = 1/2x - 1
y = 8/x
y = x + 2/5

3.
What are the x- and y-intercepts of 6x - 4y = -36?

1 Answer

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1) This is the equation for distance between two points:
d= \sqrt{( {x _(1)} - x_(2))^(2) + ( {y _(1)} - y_(2))^(2)}

Don't make it fool you, this is just a fancy translation of
{a}^(2) + {b}^(2) = {c}^(2) or the Pythogarean theorem.

The first parentheses or the x ones represents the difference between their location horizontally. Which is also a "leg".

The second or the y ones stands for the vertical difference.

Distance is the hypotenuse of those two values.

When we plug in the givens into the equation:
d = \sqrt{ {(( - 2) - 4)}^(2) + {(5 - 1)}^(2) }

Simplify:

d = \sqrt{ { (- 6)}^(2) + {4}^(2) }

d = √(36 + 16)

d = √(52)

2) The template for a "directly proportional" equation is:
y = kx where k is the constant which causes the "proportional" change.

The only one we see in the choices which is in this format is A.

3) To find x or y-intercepts, we need to plug in 0 for the other value.

For example, x-intercept of this equation is:
6x - 4 * 0 = - 36

Simplify:

6x - 0 = - 36

6x = - 36

(6x)/(6) = ( - 36)/(6)

x = - 6

So, the x-intercept is (-6, 0).

For y-intercept, the equation becomes:
6 * 0 - 4y = - 36

The zero cancels the six:
- 4y = - 36

When we divide both sides by -4:
y = 9

The y-intercept is (0, 9).
User Peter Segerblom
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