Question

Write an equation in standard form of the line that passes through (3,-7) and (9,-2)

Answer 1

The equation is on the form y=ax+b, hence a(3)+b=-7 and a(9)+b=-2. Then
3a+b=-7
9a+b=-2
Then a=5/6, b=-19/2.
The equation is y=5/6x-19/2.

Answer 2

slope = (-2 + 7)/(9 - 3) = 5/6

y = mx + b
-7 = 5/6(3) + b
b = -7 - 5/2
b = - 19/2

equation
y = 5/6x - 19/2

standard form
5/6x - y = 19/2 or 5x - 6y = 57