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)
(-12,33)
(1,-2.75)
(20,-55)
To determine if y varies directly with x, we can check if the ratio between y and x remains constant for all the given data points.
For the given data points, let's calculate the ratio of y to x:
For the point (-12, 33):
Ratio = y / x = 33 / (-12) = -11/4
For the point (1, -2.75):
Ratio = y / x = -2.75 / 1 = -11/4
For the point (20, -55):
Ratio = y / x = -55 / 20 = -11/4
From the calculations, we can see that the ratio of y to x is the same for all the data points (-11/4). Therefore, y varies directly with x.
To write the equation for direct variation, we can use the formula y = kx, where k is the constant of variation. Since we know the ratio of y to x is -11/4, we can set k = -11/4 and the equation becomes:
y = (-11/4)x