Question

determine a equação da reta que passa pelos pontos A (5,-3) e B(2,4)

Answer 1

(5, -3)

y = ax + b
-3 = 5a + b

(2, 4)

y = ax + b
4 = 2a + b (-1)
-4 = -2a - b

5a + b = -3
-2a - b = -4
3a = -7
a = $\frac{-7}{3}$

5a + b = -3
5.$\frac{-7}{3}$ + b = -3
$\frac{-35}{3}$ + b = -3
b = -3 + $\frac{35}{3}$
b = $\frac{26}{3}$

a = $\frac{-7}{3}$; 
b = $\frac{26}{3}$

y = ax + b

y = $\frac{-7x \ + \ 26}{3}$