For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.
x
-12
1
20
y
21
-1.75
-35
To determine if y varies directly with x, we need to check if the ratio of y to x remains constant for all values in the table.
Calculating the ratios for each pair of values:
For (x=-12, y=21): y/x = 21/-12 = -1.75
For (x=1, y=-1.75): y/x = -1.75/1 = -1.75
For (x=20, y=-35): y/x = -35/20 = -1.75
Since the ratio of y to x is the same (-1.75) for all values in the table, y varies directly with x.
To write the equation for direct variation, we can use the form y = kx, where k is the constant of variation.
From the table, we can see that when x=1, y=-1.75. Plugging these values into the equation, we have:
-1.75 = k * 1
Simplifying the equation:
k = -1.75
Therefore, the equation for the direct variation is:
y = -1.75x