Answer:
Ben is incorrect because the slopes of the lines between two points are not same.
Step-by-step explanation:
The given points are (2,4), (4,8) and (8,12).
If all the points lie on a straight line, then the slopes of the line joining the pair of points are same.
Slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of line joining (2,4) and (4,8).
[tex]m_1=\frac{8-4}{4-2}[/tex]
[tex]m_1=\frac{4}{2}[/tex]
[tex]m_1=2[/tex]
The slope of line joining (2,4) and (8,12).
[tex]m_2=\frac{12-4}{8-2}[/tex]
[tex]m_2=\frac{8}{6}[/tex]
[tex]m_2=\frac{4}{3}[/tex]
The slope of line joining (4,8) and (8,12).
[tex]m_3=\frac{12-8}{8-4}[/tex]
[tex]m_3=\frac{4}{4}[/tex]
[tex]m_3=1[/tex]
Since the slopes are not equal therefore these points lies on different lines.
Hence proved that ben is incorrect.
