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.
[tex] \frac{y}{x} [/tex] = 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 = [tex] \frac{6}{2} [/tex] = 3. therefore, the equation describing this direct variation is y = 3x.
k = [tex] \frac{9}{-6} [/tex] simplify it
y = [tex] \frac{-3}{2} [/tex]x
k = [tex] \frac{-1.5}{1} [/tex]
y = -1.5x
k = [tex] \frac{-12}{8} [/tex]
y = [tex] -\frac{3}{2} [/tex]x
