Question 355203
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 it's slope
 X-4Y = 4
mulitplying thru by -1
-x + 4y = -4
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4y = x - 4
{{{y = (1/4)x -4}}}   Slope of this line is {{{(1/4)}}}
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Our new line also with a slope of (1/4)
{{{y = (1/4)x +b}}}
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substituting these values(-6,-2)to solve for b
{{{ -2 = (1/4)(-6) +b}}}

{{{ -2 + (3/2) = b}}}
b = -1/2
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Equation of new line
{{{y = (1/4)x - (1/2)}}}