A line passes through the points $A,$ $B,$ and $C.$ If $A = (-2,5),$ $B = (-3,1),$ and $C = (4,y),$ then find $y.$

Answer 1

The slope of the line passing through $A$ and $B$ is
$$\frac{5-1}{-2-(-3)}=\frac{4}{1}=4.$$Therefore, the equation of this line is
$$y-5=4(x+2).$$In particular, $y = 5 + 4x.$

The slope of the line passing through $B$ and $C$ is
$$\frac{1-y}{-3-4}=\frac{y-1}{7}=4.$$Thus, $4y - 4 = 7,$ so $4y = 11,$ and $y = \boxed{\frac{11}{4}}.$