In the x-y coordinate plane, which of the following points…
To solve we first want to isolate y in the equation kx + 3y = 6.
3y = -kx + 6
y = -kx/3 + 6/3
y = (-k/3)x + 2
Now that we have the equation in the slope-intercept form of a line, we see that when x = 0, regardless what the value of k is, y is always equal to 2. In other words, the point (0,2) is always on the line regardless of what the value of k is.