Question

A linear equation exists for the following sets of ordered pairs: {(-1, 1), (0, 3), (-1/3, 7/3)}. The rule for the linear equation states that y is three more than twice x. Set up a linear equation that satisfies the rule, and use the set of ordered pairs to prove that your equation satisfies the set of coordinates.

Answer 1

From the statement:
y is three more than twice x

We can generate the equation:
y = 3 + 2x

or
y = 2x + 3

Testing the equation with the given ordered pairs:
For (-1,1)
1 = 2(-1) + 3
1 = 1 (correct!)

For (0,3)
3 = 2(0) + 3
3 = 3 (correct!)

For (-1/3, 7/3)
7/3 = 2(-1/3) + 3
7/3 = 7/3 (correct)

Answer 2

The rule of the linear equation which is 'y is three more than twice x' can be translated into y = 2x + 3. Thus, we simply use the points and subtitute it to the y and x variables.

1st point: (-1, 1)
1 = 2(-1) + 3
1 = -2 + 3
1=1

2nd point: (0, 3)
3 = 2(0) + 3
3 =3

3rd point: (-1/3, 7/3)
7/3 = 2(-1/3) + 3
7/3 = -2/3 + 3
7/3 = 7/3

All points prove the equation satifsfies the set of coordinates.