Direct and inverse variation

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as $$y = kx$$ , where $$k$$ is a non-zero constant.

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as $$y = \frac{k}{x}$$ , where $$k$$ is a non-zero constant.

Yes, it is a direct variation because it can be expressed in the form $$y = kx$$ with $$k = 2$$ .

$$k = 2$$ , since $$10 = k(5)$$ leads to $$k = \frac{10}{5} = 2$$ .

$$k = 30$$ , since $$y = \frac{k}{x}$$ gives $$15 = \frac{k}{2}$$ , leading to $$k = 15 \times 2 = 30$$ .

(0, 0), because direct variation passes through the origin.

$$y = \frac{k}{x}$$ is the equation that represents inverse variation.

$$y = 24$$ , since $$k = 4$$ and $$y = kx$$ gives $$y = 4(6) = 24$$ .

Direct variation indicates that two quantities are proportional to each other, meaning as one increases, the other increases at a constant rate.

$$y = 10$$ , since $$k = 20$$ and $$y = \frac{20}{x}$$ gives $$y = \frac{20}{2} = 10$$ .