SOLUTION: What should i do for this problem: Line through (1,-3) parallel to 2x-3y=7

Question 157184: What should i do for this problem: Line through (1,-3) parallel to 2x-3y=7
Found 2 solutions by Alan3354, checkley77:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What should i do for this problem: Line through (1,-3) parallel to 2x-3y=7
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First, find the slope of 2x-3y=7
Put it in the slope-intercept form, y = mx + b
2x-3y=7
-3y=-2x+7
3y=2x-7
y = (2/3)x -7/3
The slope, m, is 2/3
Parallel lines have the same slope, in the case 2/3
Use the slope-intercept form again:
y-y1 = m*(x-x1)
y-(-3) = (2/3)*(x-1)
y+3 = (2/3)*(x-1) = 2x/3 - 2/3
y = 2x/3 - 11/3 slope-intercept form
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3y = 2x - 11
2x - 3y = 11 standard form

Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Line through (1,-3) parallel to
2x-3y=7
-3y=-2x+7
y=-2x/-3+7/-3
y=2x/3-7/3 (RED LINE)
This line has a slope=2/3. THus the parallel line will also have a slope=2/3.
replace x & y by (1,-3) & m by the slope=2/3 in the line equation Y=mX+b & SOLVE FOR THE Y INTERCEPT (b).
-3=2/3*1+b
-3=2/3+b
b=-3-2/3
b=(-3*3-2)/3
b=(-9-2)/3
b=-11/3 IS THE Y INTERCEPT.
Y=2X/3-11/7 (GREEN LINE)
(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 2x/3 -7/3 and 2x/3 -11/7).
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