To calculate hte possible values of y you have to apply the Pythagoras theorem:
[tex]a^2+b^2=c^2[/tex]Where
c will be the distance between the given points, and the hypothenuse of a right triangle
a will be the base of a theoretical triangle below the hypothenuse, you calculate it as (x2-x1)
b= will be the heigth of said triangle, you calculate it using the y-coordinates (y2-y1)
So:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ c=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]Replace the expression with the given measurements to calculate the y-coordinate of the first point:
[tex]\begin{gathered} c=\sqrt[]{(3_{}-(-2))^2+(-7-y)^2} \\ 13=(3+2)+(-7-y) \\ 13=5-7-y \\ 13=-2-y \\ 13+2=-y \\ -15=y \end{gathered}[/tex]The possible values for y, since its
