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# finding coordinates on a line

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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.

Aug 1, 2017

#1
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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. Aug 1, 2017
edited by hectictar  Aug 2, 2017

#1
+3

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. hectictar Aug 1, 2017
edited by hectictar  Aug 2, 2017