Question

For the data in the​ table, tell whether y varies directly with x. If it​ does, write an equation for the direct variation.

x , y
-12 , 21
1 , -1.75
16, -28
Write an equation for the direct variation. Select the correct choice and fill in any answer boxes in your choice below.

y=

(Use integers or decimals for any numbers in the​ expression.)

Answer 1

To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all values in the table.

For the given values, we can calculate the ratios:

21 / -12 = -1.75

-1.75 / 1 = -1.75

-28 / 16 = -1.75

Since the ratio of y to x is consistent at -1.75 for all values, we can conclude that y varies directly with x.

Now, we need to write the equation for the direct variation. In direct variation, the equation takes the form y = kx, where k is the constant of variation. Since the ratio is -1.75, the equation for the direct variation is:

y = -1.75x