Direct variation:
When the two variables are related in such a way that the ratio of their values remains the same, the two variables are said to be having direct variation.
Or we can say that, if A is always twice as much as B, then they vary directly.
If y varies directly as x, the graph of all the points which describe this relationship is a line going through the origin (0, 0) the slope of which is called as constant of the variation. That is because each variables is a constant multiple of the other.
1) Expressing Direct Variation an Equation
The common form of our sample equation y = 6x is written y = kx, where k is the constant of variation. Or we can say that, the value of k does not change.
2) Algebraic Interpretation of Direct Variation
For an equation of the form y = kx, multiplying x by some fixed amount also multiplies y by the SAME FIXED AMOUNT. For example, as the perimeter P of a square varies directly as the length of 1 side of a square, we can say that P = 4s, where the number 4 represents the 4 sides of a square and s represents the length of 1 side.
3) Geometric Interpretation of Direct Variation
The equation y = kx is a special case of the linear equation
y = mx + b, here b = 0. (the equation y = mx + b is the slope-intercept form where m is the slope and b is y-intercept). Anyway, a line through the origin (0,0) represents a direct variation between y and x. Slope of the line is constant of variation. Conversely in the equation
y = mx + b, m is the constant of variation.
A relationship in between 2 variables in which 1 is a constant multiple of the other. Particularly when 1 variable changes the other changes in proportion to the 1st.
When b is directly proportional to a, the equation is of the form b = ka (here k is a constant).
An equation y = kx is a direct variation. The quantities represented by x and y are proportional, and k is the constant of variation.
We can represent any ratio, rate, or conversion factor with the direct variation. By using a direct variation graph is 1 way to solve proportions. A relationship in between 2 variables in which their ratio remains constant.