Question

Hello i have some questions i do not understand.

Answer 1

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:
$d = \sqrt{ { (- 6)}^{2} + {4}^{2} }$
$d = \sqrt{36 + 16}$
$d = \sqrt{52}$

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: $6x - 4 \times 0 = - 36$

Simplify:
$6x - 0 = - 36$
$6x = - 36$
$\frac{6x}{6} = \frac{ - 36}{6}$
$x = - 6$

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

For y-intercept, the equation becomes: $6 \times 0 - 4y = - 36$

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

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

The y-intercept is (0, 9).