Question

three points of a function are graphed.
which statement describes the function through the points?
the function is a direct variation function with a constant of variation of 1.5.
the function is a direct variation function with a constant of variation of 1.8.
the function is linear but is not a direct variation function.
the function is not a linear function.
(graph with points (10, 18), (14, 24), (18, 30))

Explanation:

Step1: Check if linear (calculate slopes)

Slope between (10,18) and (14,24): $\frac{24 - 18}{14 - 10} = \frac{6}{4} = 1.5$
Slope between (14,24) and (18,30): $\frac{30 - 24}{18 - 14} = \frac{6}{4} = 1.5$
So, the function is linear (constant slope 1.5).

Step2: Check direct variation (passes through origin?)

Direct variation: $y = kx$ (passes through (0,0)).
Using $y = 1.5x$, when $x = 10$, $y = 15
eq 18$. So, it does not pass through the origin. Thus, not direct variation.

Answer:

The function is linear but is not a direct variation function.