Question

Given: -x+y= 15. 3 Which of the following are ordered pairs of this equation? {(-3, 14),(0,15).(3.16)} {(16.-3) (15, 0) (14.3)} {(-3, 16).(0.15).(3, 14)

Answer 1

To determine if a point is in a line we have to substitute the values of x and y in the equation, if the equation holds then the point is in the line.

We have the equation

`-x+y=15`

Let's see if the first set of points is in the line.

Set {(-3,14), (0,15), (3,16)}.

The first point is (-3,14), in this case x=-3 and y=14. Plugging the values in the equation we have:

`\begin{gathered} -(-3)+14=15 \\ 3+14=15 \\ 17=15 \end{gathered}`

Since this is not true, the point (-3,14) is not in the line. Therefore this set is not in the line.

Set {(16,-3), (15,0), (14,3)}.

Let's see the first point, (16,-3).

`\begin{gathered} -(16)+(-3)=15 \\ -16-3=15 \\ -19=15 \end{gathered}`

since this is not true, the point (16,-3) doesn't lie in the line. Therefore this set of points is not in the line.

Set {(-3,16), (0,15), (3,14)}.

The first point is (-3,16). Then

`\begin{gathered} -(-3)+16=15 \\ 3+16=15 \\ 19=15 \end{gathered}`

since this is not true, the point (-3,16) doesn't lie in the line. Therefore this set of points is not in the line.

Note:

The only point that it is in the line of the ones given is the point (0,15), since:

`\begin{gathered} -0+15=15 \\ 15=15 \end{gathered}`