the equation of a line is x + 3y - 24 = 0. write the coordinates of a point on the line for each of the following conditions:
a) the x-coordinate is equal to the y-coordinate.
b) the x-coordinate is three times as great as the y-coordinate.
c) the y-coordinate is four greater than the x-coordinate.
+9466 x + 3y - 24 = 0
a) Plug in y for x and solve for y .
y + 3y - 24 = 0
4y - 24 = 0
4y = 24
y = 6
The coordinate = (x, y) = (y, y) = (6, 6)
b) Plug in 3y for x and solve for y .
(3y) + 3y - 24 = 0
6y - 24 = 0
6y = 24
y = 4
The coordinate = (x, y) = (3y, y) = (3*4, 4) = (12, 4)
c) Plug in x + 4 for y and solve for x .
x + 3y - 24 = 0
x + 3(x + 4) - 24 = 0
x + 3x + 12 - 24 = 0
4x - 12 = 0
4x = 12
x = 3
The coordinate = (x, y) = ( x, x + 4 ) = ( 3, 3 + 4 ) = (3, 7)
The graph here verifies that these coordinates are points on the line. 
+9466 x + 3y - 24 = 0
a) Plug in y for x and solve for y .
y + 3y - 24 = 0
4y - 24 = 0
4y = 24
y = 6
The coordinate = (x, y) = (y, y) = (6, 6)
b) Plug in 3y for x and solve for y .
(3y) + 3y - 24 = 0
6y - 24 = 0
6y = 24
y = 4
The coordinate = (x, y) = (3y, y) = (3*4, 4) = (12, 4)
c) Plug in x + 4 for y and solve for x .
x + 3y - 24 = 0
x + 3(x + 4) - 24 = 0
x + 3x + 12 - 24 = 0
4x - 12 = 0
4x = 12
x = 3
The coordinate = (x, y) = ( x, x + 4 ) = ( 3, 3 + 4 ) = (3, 7)
The graph here verifies that these coordinates are points on the line.
