Question

Which of the following sets of ordered pairs will create a straight line?

O
(3,6) (6, 12) (12, 19) (15, 13)
(-2,4), (-1,8), (0, 12), (1, 16)
(2,9), (1,7), (0, -14), (-1,20)

Answer 1

(-2,4), (-1,8), (0, 12), (1, 16) is a set of points in a straight line

Explanation:

Points On A Line

If we are given a set of points (x1,y1),(x2,y2)(x3,y3),... they are part of a line if, between each pair of them, the slope is constant. The slope of a line, given two points, is

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

We are given these sets of points

(3,6) (6, 12) (12, 19) (15, 13)

(-2,4), (-1,8), (0, 12), (1, 16)

(2,9), (1,7), (0, -14), (-1,20)

Let's try the first one

(3,6) (6, 12) (12, 19) (15, 13)

The first slope is

`\displaystyle m_1=(12-6)/(6-3)=2`

The next slope is

`\displaystyle m_2=(19-12)/(12-6)=(7)/(6)`

Both values are different, so the set is not part of a line

Now for the second set

(-2,4), (-1,8), (0, 12), (1, 16)

Here are the slopes

`\displaystyle m_1=(8-4)/(-1+2)=4`

`\displaystyle m_2=(12-8)/(0+1)=4`

`\displaystyle m_3=(16-12)/(1-0)=4`

All of them are equal, so these points lie in the same line

The third set of points results are

`\displaystyle m_1=(7-9)/(1-2)=2`

`\displaystyle m_2=(-14-7)/(0-1)=21`

The slopes are different. This set is not part of a line