Question

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

Answer 1

$A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\the\ slope:m=\dfrac{y_B-y_A}{x_B-x_A}$

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