Explanation:
y = 1/4 x
do you know what point coordinates are ?
they are "ordered pairs" of x and corresponding y values.
and do you know what a function is ?
a function "processes" an input x value and creates a corresponding y output value (the functions result).
a point is part of a function and on the graph of the function, if the x coordinate of the point leads to the y coordinate of the point as functional result of the function.
in other words, we take the x values and check, if the resulting y values are identical with the y coordinates.
(4, 1)
y = 1/4 × 4 = 4/4 = 1
match, this is a point on the graph.
(4, 0)
the same x value as before, leads to the same y value (1) as before. so, no match.
(8, 2)
y = 1/4 × 8 = 8/4 = 2
match, this is a point on the graph.
(0, 0)
y = 1/4 × 0 = 0
match, this is a point on the graph.
(1, 2)
y = 1/4 × 1 = 1/4
no match to 2. not a point on the graph.
(5, 6)
y = 1/4 × 5 = 5/4
no match to 6. not a point on the graph.