Question

The equation of a line?

passes through (-2,5) and is parallel to y-2/3x+1

would the answer be y=2/3x+19/3

Answer 1

y - 5 = m[ x - ( - 2 ) ] is the "point-slope" form of your staright - line equations;
y - 5 = m( x + 2 ) ;
But, your line is parallel to y = ( 2 / 3 )x + 1;
m = 2 / 3;
Finally, y - 5 = ( 2 / 3)( x + 2);
y = 5 + ( 2 / 3)x + 4 / 3;
y = ( 2 / 3 )x + 15 / 3 + 4 / 3 ;
y = ( 2 / 3 )x + 19 / 3.