Answer:
C)
Step-by-step explanation:
in order to understand which triangle would lie on the given line we should figure out the slope of the given line first
remember that,
[tex] \displaystyle m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}} [/tex]
from the graph let's take two points where the line passes i.e (0,0) and (4,6)
substitute:
[tex] \displaystyle m = \frac{6- 0}{ 4 - 0} [/tex]
simplify substraction:
[tex] \displaystyle m = \frac{6 }{ 4 } [/tex]
reduce fraction:
[tex] \displaystyle m = \frac{3}{ 2} [/tex]
now we need a triangle which tan ratio equal to the slope in that case we can consider the third triangle
[tex] \displaystyle \tan( \theta) = \frac{30}{20} [/tex]
reduce fraction:
[tex] \displaystyle \tan( \theta) = \frac{3}{2} [/tex]
since the tan ratio of the third triangle equal to the slope of the line
hence, our answer is c
