1) This is the equation for distance between two points: [tex]d= \sqrt{( {x _{1}} - x_{2})^{2} + ( {y _{1}} - y_{2})^{2}}[/tex]
Don't make it fool you, this is just a fancy translation of [tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex] 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: [tex]d = \sqrt{ {(( - 2) - 4)}^{2} + {(5 - 1)}^{2} } [/tex]
Simplify:
[tex]d = \sqrt{ { (- 6)}^{2} + {4}^{2} } [/tex]
[tex]d = \sqrt{36 + 16} [/tex]
[tex]d = \sqrt{52} [/tex]
2) The template for a "directly proportional" equation is: [tex]y = kx[/tex] 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: [tex]6x - 4 \times 0 = - 36[/tex]
Simplify:
[tex]6x - 0 = - 36[/tex]
[tex]6x = - 36[/tex]
[tex] \frac{6x}{6} = \frac{ - 36}{6} [/tex]
[tex] x = - 6[/tex]
So, the x-intercept is (-6, 0).
For y-intercept, the equation becomes: [tex]6 \times 0 - 4y = - 36[/tex]
The zero cancels the six: [tex] - 4y = - 36[/tex]
When we divide both sides by -4: [tex]y = 9[/tex]
The y-intercept is (0, 9).
