Question

Three points of a function are graphed.

A coordinate plane with 3 points plotted at (10, 18), (14, 24), and (18, 30).
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.

Answer 1

Answer:

The correct answer is The function is a direct variation function with a constant of variation 1.5.

Step-by-step explanation:

One way to see if this is a linear function is to see by how much the x and y increase each time:

x   |  y

10 | 18

14 | 24

18 | 30

X is increasing by 4 each time, and y is increasing by 6. This is a linear function. Divide the y by the x to get the slope.

6 ÷ 4 = 1.5

This is a linear function and its slope is 1.5.

Hope this helps,

♥A.W.E.S.W.A.N.♥

Answer 2

Answer:

The function is a direct variation function with a constant of variation of 1.5.

Step-by-step explanation:

A direct variation function can be seen has a linear function, which has a proportional relationship between variables, which ratio is the slope of the line.

If we see all three points, the increases a constant number.

10,14,18: here you can see that x-variable is increasing constantly by 4.

18, 24, 30: here you can see that y-variable is increasing constantly by 6.

So, if we use to points and the definition of slope, we have:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{30-18}{18-10}=\frac{12}{8}=1.5$

Therefore, the ratio of change or the constant of variation is 1.5.

So, the right answer is the first one.