Question 662639
You need to find the slope of the given line
(1) 3x + 5y = 10 which is given in the standard form
(2) Ax + By = C whose slope is given by
(3) m = -A/B which, for the given line, yields
(4) m = -3/5.
To be parallel to this line, the new line must have the same slope. In the slope-intercept form we want
(5) y = -3/5x + b. 
We deterine the value of b by satisfying the second condition that it must pass through P(2,3). Substituting P into (5) yields
(6) 3 = -3/5(2) + b
Solve (6) for b gives
(7) b = 21/5
Your new line is 
(8) y = -(3/5)x + 21/5
Let's use P(2,3) to check the equation.
Is (3 = -(3/5)*2 + 21/5)?
Is (3 = -6/5 + 21/5)?
Is (3 = 15/5)?
Is (3 = 3)? Yes
Answer: The new line is y = -(3/5)x + 21/5