Question 1120389
you want the line parallel to 3x + 5y = 17 that passes through the point (-2,3).


if the line is parallel, it will have the same slope.


convert 3x + 5y to slope intercept form of y = mx + b.


subtract 3x from both sides of the equation to get 5y = -3x + 17


divide both sides of the equation by 5 to get y = -3/5 * x + 17/5.


the slope is -3/5.


your parallel line must have the same slope.


your parallel line with have a slope of -3/5.


the point slope form of your equation will be (y - y1) = m * (x - x1).


your slope is equal to m which is equal to -3/5.
your point is equal to (-2,3) which is equal to (x1,y1).


when m = -3/5 and y1 is equal to 3 and x1 is equal to -2, the point slope form of the equation becomes:


(y - 3) = -3/5 * (x + 2)


multiply both sides of this equation by 5 to get:


5 * (y - 3) = -3 * (x + 2)


simplify to get:


5y - 15 = -3x - 6


add 3x to both sides of this equation and add 15 to both sides of this equation to get:


5y + 3x = 15 - 6


simplify and place x variable ahead of y variavble to get:


3x + 5y = 9


subtract 9 from both sides of this equation to get:


3x + 5y - 9 = 0


that's your solution.