Question 409971
 <pre><font size = 3 color = "indigo"><b>
Hi

A line that passes through the origin and is parallel to x + y = 6.
*[tex \LARGE\ Using \ the \ standard \ slope-intercept \ form \ for \ an \ equation \ of \ a  \ line \ y = mx + b ] 
*[tex \LARGE\ where \ m \ is \ the \ slope \ and \ b \ the \ y-intercept]
 x + y = 6  OR y = -x + 6  |slope m = -1.  Parallel lines have identical slopes
New Line:
 y = -x + b   |using ordered pair Pt(0,0) to solve for b
 0 = 0 + b
 0 = b 
  y = -x   |written in standard from: x + y = 0
{{{drawing(300,300,   -10,10,-10,10,
 grid(1),
circle(0, 6,0.4),
graph( 300, 300, -10,10,-10,10,0,-x+6,-x))}}}