Which of the following represents a linear equation in two variables? 

Consider alternative 1). 

$$3p^{\frac{3}{2}}+7q\sqrt[ ]{p}=8\sqrt[ ]{p}$$ 

$$\Rightarrow 3p\sqrt[ ]{p}+7q\sqrt[ ]{p}=8\sqrt[ ]{p}$$ 

$$\Rightarrow \left(3p+7q\right)\sqrt[ ]{p}=8\sqrt[ ]{p}$$ 

$$\Rightarrow 3p+7q=8$$ 

The equation 3p + 7q = 8 is a first degree equation and consists of two variables, p and q. 

Thus, it is a linear equation in two variables. 

Consider alternative 2). 

$$\frac{3x^2}{4y}=\frac{7x^2}{5}$$ 

$$\Rightarrow \frac{3}{4y}=\frac{7}{5}$$ 

$$\Rightarrow 28y-15=0$$ 

Since the equation 28y − 15 = 0 consists of only one variable, y, it is not a linear equation in two variables. 

Consider alternative 3). 

$$\frac{9a}{2b}=\frac{11b}{13a}$$ 

$$\Rightarrow 9a\times 13a=11b\times 2b$$ 

$$\Rightarrow 117a^2-22b^2=0$$ 

The equation $$117a^2-22b^2=0$$ consists of two variables, a and b, but its degree is 2. 

Hence, it is not a linear equation in two variables. 

Consider alternative 4). 

The equation 15x + 17 = 0 consists of only one variable x, so it is not a linear equation in two variables.