Question 157184
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( 300, 200, -6, 5, -10, 10, 2x/3 -7/3, 2x/3 -11/7) }}} (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).