ap

given a, x₁, x₂ ,b are in ap ,so there are total 4numbers.

so a4th = a1+(n-1)d    where a1=a , n=4 and d=(x_2-x₁)

therefore b=a+3(x_2-x₁)

=> (x_2-x₁) = (b-a)/3       simillarly given a , y_1, y₂, y_3, b are in ap ,so we will get (y_2-y₁) = (b-a)/4 

therefore , (y_2-y₁) / (x_2-x₁)  = (b-a)/4 / (b-a)/3  = 3/4    answer