the equation of a straight line which passes through the point (-3 , 5) such that the portion of it between the axes is divided by the point in the ratio 5:3 (reckoning from x- axis ) will be what?

Let the points where the line intersects the axes be (a,0) and (0,b),
and the point which divides the line in ratio 5:3 be (h,k)

According to the question

y applying section formula

[3(a)+5(0)/8 , 3(0)+5(b)/8] = (h,k)

3a/8 = h
5b/8 = k
a = 8h/3
b = 8k/5

Putting in value of h and k as (-3,5) respectively,

we get a = -8 and b = 8

using intercept form - x/a + y/b = 1 (general eqn.)
we get by putting values of a and b -->
x/-8 +y/8 = 1

-x + y = 8

x - y + 8 = 0

This was the required equation of line