For the data in the table, does y vary directly with x? if it does, write an equation for the direct variation. x = -6 , 1 , 8 y = 9 , -1.5 , -12

X = -6    y = 9
x =  1    y = -1.5
x =  8    y = -12

the statement "y varies directly with x" means that when x increases, y increases by the same factor. in other words, y and z always have the same ratio.

= k

where k is the constant variation. the relationship between x and y can also be expressed as: y = kx

since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. for example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k =  = 3. therefore, the equation describing this direct variation is y = 3x.

k =  simplify it
y = x

k = 
y = -1.5x

k = 
y = x