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) This is the equation for distance between two points:

Don't make it fool you, this is just a fancy translation of 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:

Simplify:




2) The template for a "directly proportional" equation is: 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:

Simplify:





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

For y-intercept, the equation becomes:

The zero cancels the six:

When we divide both sides by -4:

The y-intercept is (0, 9).