Question 355205
Hi,
*Note: parallel lines have the same slope. (they "slant" in the same direction so they do not cross one another: they are parallel)
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The slope intercept equation for a line is y = mx + b where m is the slope and y -intercept (the point where the line crosses the y axis)
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solving equation given for y, in order to find its slope
 2X+Y = 9 

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y = -2x + 9        Slope of this line is {{{(-2)}}} 

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Our new line also with a slope of -2 (slope is negative, both lines slope to the left)
{{{y = -2x +b}}}
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substituting these values (1,1))to solve for b
{{{ 1 = -2  +b}}}

{{{ 1 + 2 = b}}}
b = 3
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Equation of new line
{{{y = -2x   + 3}}}

{{{ graph( 300, 300, -10, 10, -10, 10, -2x + 3,-2x + 9) }}}