Question

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

Answer 1

Answer:

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

Step-by-step 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

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

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

$\displaystyle m_1=\frac{12-6}{6-3}=2$

The next slope is

$\displaystyle m_2=\frac{19-12}{12-6}=\frac{7}{6}$

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

$\displaystyle m_1=\frac{8-4}{-1+2}=4$

$\displaystyle m_2=\frac{12-8}{0+1}=4$

$\displaystyle m_3=\frac{16-12}{1-0}=4$

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

The third set of points results are

$\displaystyle m_1=\frac{7-9}{1-2}=2$

$\displaystyle m_2=\frac{-14-7}{0-1}=21$

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