Question

you are given an equation of a line and a point and told to use substitution to determine whether the point is on the line

Answer 1

Fine !

-- Take the 'x' of the point and write it in place of 'x' in the equation.
-- Then take the 'y' of the point and write it in place of the 'y' in the equation.
-- Now the equation has nothing but numbers in it, and it says that the numbers
on the left side are equal to the numbers on the right side.
-- Look at it and see if the statement is true.
-- If true, then the point is on the line.
-- If false, then the point is not on the line.

Examples:

1). Equation . . . y = 6x + 1
Point. . . . . . . (3, 19) (x=3, y=19)

Plug the point into the equation: y = 6x + 1
19 = 6(3) + 1
19 = (18) + 1
19 = 19
The statement is true.
The point is on the line.

2). Equation . . . 2x + 3y = 9
Point . . . . . . . (1, 2) (x=1, y=2)

Plug the point into the equation: 2 x + 3 y = 9
2(1) + 3(2) = 9
2 + 6 = 9
8 = 9
The statement is false.
The point is NOT on the line.