Find the equation of line which contains the point (-2,3) and is parallel to the line 3x+5y=17. ( write the numerical coefficient of each term to complete the required equation )

Question

Please help. Thank you

Answer 1

Parallel lines have the same slope, so the slope is -3/5, because 5y=17-3x, y=-3x/5+17/5.

The equation of the line is y=-3x/5+a where we have to find a by plugging in the given point:

3=6/5+a, so a=9/5 and y=-3x/5+9/5, which can be written 3x+5y=9 to match its parallel counterpart.