If y varies directly as x and y=14 when x= 3.5 what is the constant of variation

Hey there! Direct variation, a concept commonly applied to linear equations.

The constant of variation is a concept which simply refers to the change in y, based on the change in x. If this change is constant, then it is a constant of variation.

You can find the constant of variation (usually referred to as 'k') by dividing any point's y-value by its x-value.

In this instance, we have the point (3.5, 14)

14 / 3.5 = 4

The constant of variation for this equation would be 4.

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you