Question

Indicate in standard form the equation of the line passing through the given points.

B(0, 0), C(4, -4)

Answer 1

Standard form: y=mx+b, where m=slope and b=y-intercept.
Using the equation m = (y2-y1)/(x2-x1) you can plug in the two points. Solving that you should get m = -1.
After that, you can plug in one of the points you are given into the equation we now have y=(-1)x+b and solve for b.
Using (4,-4) we get -4=(-1)(4)+b. b=0.
Looking at the points you are given you can tell that the y intercept will be 0, as the orgin is one of the points given (0,0).
So you end up getting y=-x as the equation of your line.