Answer :
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
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
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
[tex]\displaystyle m_1=\frac{12-6}{6-3}=2[/tex]
The next slope is
[tex]\displaystyle m_2=\frac{19-12}{12-6}=\frac{7}{6}[/tex]
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
[tex]\displaystyle m_1=\frac{8-4}{-1+2}=4[/tex]
[tex]\displaystyle m_2=\frac{12-8}{0+1}=4[/tex]
[tex]\displaystyle m_3=\frac{16-12}{1-0}=4[/tex]
All of them are equal, so these points lie in the same line
The third set of points results are
[tex]\displaystyle m_1=\frac{7-9}{1-2}=2[/tex]
[tex]\displaystyle m_2=\frac{-14-7}{0-1}=21[/tex]
The slopes are different. This set is not part of a line