Question 681915
Starting with 2x-3y=7
isolate the y variable
2x - 3y + 3y = 7 + 3y
2x = 7 + 3y
2x - 7 = 7 + 3y - 7
3y = 2x - 7
y = {{{(2/3)x - (7/3)}}}
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The slope of this line is {{{2/3}}} and a parallel line will have the SAME slope.
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Use the slope and point
y - 6 = {{{2/3}}}(x--2)
y - 6 = {{{(2/3)x + (2/3)(2)}}}
y = {{{(2/3)x + (4/3) + 6}}}
y = {{{(2/3)x + (4/3) + 6(3/3)}}}
{{{highlight_green(y = (2/3)x + 22/3)}}}