Aline and a circle intersect at the points a and b.
use the equations below to find the coordinates of the points of intersection a and b.
y =x+4
(x−3) ^ 2 + (y−5) ^ 2 = 34
can i have a step by step explanation because im so confused

  A = (-2, 2)

  B = (6, 10)

Step-by-step explanation:

The points of intersection on the graphs of these equations are the values of (x, y) where both equations are satisfied. There are several ways to find those points. One of my favorite is to use a graphing calculator. (See attached)

Quite often it is reasonable and feasible just to use the expression given for y to substitute into the second-degree equation. Doing that gives ...

  (x -3)^2 +((x+4) -5)^2 = 34 . . . . . . . x+4 is substituted for y

  x^2 -6x +9 +x^2 -2x +1 = 34 . . . . . eliminate parentheses

  2x^2 -8x -24 = 0 . . . . . . . . . . . . . . collect terms, subtract 34

  x^2 -4x -12 = 0 . . . . . . . . . . . . . . . . divide by 2

  (x -6)(x +2) = 0 . . . . . factor

  x = 6 or -2 . . . . . . . . values of x that satisfy this equation*

Corresponding values of y are ...

  y = x+4 = 6+4 = 10 . . . for x=6

  y = -2+4 = 2 . . . . . . . . for x = -2

The points where the graphs intersect are ...

  {(6, 10), (-2, 2)}

Which is A and which is B is unknown (and probably doesn't matter). Above, they are listed with the smallest x-coordinate first.