Explanation:
the parallel line is defined as
5y - 3x = 10
let's bring it into a slope-intercept form to see the slope directly :
y = mx + b
"m" being the slope, "b" being the y-intercept (the y-value of the point where the line crosses the y-axis; the x- coordinate of any point on the y-axis is 0).
so,
5y - 3x = 10
5y = 3x + 10
y = ⅗x + 10/5 = ⅗x + 2
the slope of that line is therefore ⅗.
remember, the slope is the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
that means for our given 2 points (as parallel lines must have the same slope), as I see in a line AB B as the endpoint (but we could also do the differences the other way around) :
(-8 - -5)/(2 - a) = 3/5
(-8 + 5)/(2 - a) = 3/5
-3/(2 - a) = 3/5
the slope has to be positive, because 3/5 is positive.
that means, as the numerator is negative (-3), the denominator has to be negative too (as -/- = +).
therefore,
2 - a = -5
2 = a - 5
a = 2 + 5 = 7
the point is therefore (7, -5).