Question

Which function has the greatest constant of variation? A x 8 9 10 11 y 20 22. 5 25 27. 5 B x 1 2 3 4 y 3. 2 6. 4 9. 6 12. 8 C On coordinate plane C, a line goes through points (0, 0) and (3, 1). D On coordinate plane D, a line goes through points (0, 0) and (1, 2). A B C D.

Answer 1

You can use the given data and points to form equation of lines. And use them to find the slope(the constant of variation)

The function that has the greatest constant of variation is of function B

Option B: B

How to get the slope intercept form of a straight line equation?

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

$y = mx +c$

What is the equation of a line passing through two given points in 2 dimensional plane?

Suppose the given points are $(x_1, y_1)$ and $(x_2, y_2)$ , then the equation of the straight line joining both two points is given by

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\y = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1) + y_1\\\\y = \dfrac{y_2 - y_1}{x_2 - x_1}x + y_1 -\dfrac{y_2 - y_1}{x_2 - x_1}x_1$

Thus, comparing it with slope intercept form y = mx + c, we get

$m = \dfrac{y_2 - y_1}{x_2 - x_1} = slope\\\\c = y_1 - \dfrac{y_2 - y_1}{x_2 - x_1}x_1$

Using the data given and the above facts to find the intended function

Calculating slope of all functions one by one

• Function A:

x = 8,9,10,11, and y = 20, 22.5, 25, 27.5

Two points (8,20), (9, 22.5) are enough.

The slope is

$m =\dfrac{y_2 - y_1}{x_2 - x_1}= 2.5$

• Function B:

x =  1, 2, 3, 4 and  y  = 3.2, 6.4, 9.6, 12.8
Two points (1,3.2), (2,6.4) are enough.

The slope  is

$m = \dfrac{y_2 - y_1}{x_2 - x_1}= 3.2$

• Function C:

Two points are (0,0,), (3,1)

The slope is

$m = \dfrac{y_2 - y_1}{x_2 - x_1}= \dfrac{1}{3}$

• Function D:

Two points are (0,0), (1,2)

The slope is

$m= \dfrac{y_2 - y_1}{x_2 - x_1}= 2$

Thus, the biggest constant of variation is of function B.

Option B: B

Learn more about constant of variation here:

https://brainly.com/question/13977805