Question

Whoever helps, gets a medal.

Which of the following coordinates exists on the line y=2x+4?

A. (-3,-2)
B. (-1,3)
C. (1,5)
D. (2,4)

Answer 1

test each choice. the first number in the pair is the x value, the 2nd number is the y

Answer 2

I get B, but i don't know if that is right.

Answer 3

When we talk about a point belonging to any geometric place in Analytic Geometry we mean a point that satisfies the equality.
Meaning that wether we have a general formula or a explicit form it will satify the equation that represents the geomteric place.
So, if we have a general line and a general point:
\[r) Ax+By+C=0\]
\[P(x_p , y_p )\]
\[P \in r <=> A( x_p) + B ( y_p) +C =0\]
What I wrote in the last parts reads as: " point 'P' belong in line 'r' only if the line ecaluated in the point equals zero".
So, all you do is take the coordinates of the point and place them on the equation of the line.
I'll do an exaple with the second option:
\[y=2x+4\]
on the point A(-1,3).
Let's first take the line to it's general form, so we can see more clear if it belongs or not:
\[-2x+y-4=0\]
And instead of "x" we will plug the value "-1" and instead of "y" we'll plug "3":
\[-2(-1)+(3)-4=0\]
Doing a little arithmetic and ordering up:
\[2+3-4=0\]
\[5-4=0\]
\[1 \neq 0\]
Now, I did not get 0 on the left side so that means that the 2nd given point is not a point that belong in the line.
You can do the same with the others in order to solve the problem.