Question

Find the value of "a" such that the slope between the point (-4, 5) and (3, a) is 2/3.

Answer 1

`A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\the\ slope:m=(y_B-y_A)/(x_B-x_A)`


`(-4;\ 5);\ (3;\ a);\ m=(2)/(3)\\\\subtitute:\\\\(a-5)/(3-(-4))=(2)/(3)\\\\(a-5)/(7)=(2)/(3)\ \ \ \ \ |cross\ multiply\\\\3(a-5)=7\cdot2\\\\3a-15=14\ \  \\ |add\ 15\ to\ both\ sides\\\\3a=29\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{a=(29)/(3)}`