When the variables x and y have a direct variation relationship, they are proportional, and the equation of this function is:
y = mx
Where m is the slope of the line
You can notice that the point (0,0) also known as the origin, is part of the line.
The other point (shown in the grid) is (3,4).
Answer: 2. (3,4) or (0,0)
In this case, both points are evident because one of them (3,4) is given, and the other (0,0) is trivial for a direct relationship.
But, what if we are given a point such as (6,8) or (-9,-12). Are they part of the direct variation?
That is where we need to use the equation:
y = mx
We need to find the value of m, by using the given point (3,4):
4 = m(3)
Solving for m:
m = 4/3, thus:
y = 4/3 x
1) Checking the point (-6,-8):
-8 = 4/3 (-6)
Operating:
-8 = -24/3
-8 = -8
Point (-6,-8) is part of the equation.
Checking the point (-5,-6) does not pass the test.
2) Checking the point (0,0)
0 = 4/3 (0)
0 = 0
The equality stands, thus (0,0) is part of the equation.
Point (3,4) is also part of the equation, but it's given in the graph
3) Testing (-4,-3):
-3 = 4/3 (-4)
-3 = -16/3
This statement is false, thus (-4,-3) is not part of the equation.
Testing (-8,6):
6 = 4/3 (-8)
6 = -32/3
Thus (-8,6) is not part of the equation.