Question

How do you determine whether (6,2) is on the line y=1/2x+2

Answer 1

If the point
`(6,2)` does satisfy the equation,
`y = (1)/(2)x +2\\`, the point is on the line. Otherwise it's not.

Explanation:

Points that are on the line actually satisfy the equations of their respective lines. If the point
`(6,2)` does satisfy the equation,
`y = (1)/(2)x +2\\`, the point is on the line. Otherwise it's not.

Testing if
`(6,2)` is on the line,
`y = (1)/(2)x +2\\`:

`y = (1)/(2)x +2 \\ 2 \stackrel{?}{=} (1)/(2)(6) +2 \\ 2 \stackrel{?}{=} 3 +2 \\ 2 \stackrel{?}{=} 3 +2 \\ 2 \stackrel{?}{=} 5 \\ 2 \\eq 5`

The point
`(6,2)` does not satisfy the equation,
`y = (1)/(2)x +2\\`, so the point is not on the line.

Answer 2

Graph the line y=1/2x+2 then check the points.

Explanation:

If I go on desmos, or just by hand and graph y=1/2x+2, I can see the points it goes through. Once I graph my equation, I will specifically type another coordinate "(6,2)" to see if it is directly in my line. For your equation, (6,2) is not in the line of y=1/2x+2.

I really hope this helps, ask anything else if needed.