Question

"Which of the following represent(s) an equation of the line passing through the points A(5, 6) and B(4, 8)? Select all that apply."
a. y = -2x – 4
b. y = -2x + 16
c. y – 6 = -2(x – 5)
d. 2x + y = 16
e. 2x + y = -16

Answer 1

Consider this option:
way_1:
to substitute the given coordinates of A(5;6) and B(4;8) in every equation. Only 2x+y=16 belongs to the given points.
way_2:
to make up the equation of the line using coordinates of points A and B:
rule:
$\frac{x-x_A}{x_B-x_A}= \frac{y-y_A}{y_B-y_A}$
$\frac{x-5}{-1} = \frac{y-8}{2} \ or \ 2x+y=16$

answer: b;c;d.