## What is the constant of variation k of the direct variation y=kx through (5,8)?

The constant of variation k of the direct variation y=kx through (5,8) is 8/5.

## How to calculate the constant of variation k

In order to calculate the constant of variation k of the direct variation equation y=kx, you need to have at least two points on the graph. In this case, we have the points (5,8) and (8,11). To calculate k, you will take the slope of the line passing through these points. The slope is calculated by finding the difference in y-values and then divide it by the difference in x-values. In this case, the slope would be 3/3=1. Therefore, k=1.

### Formula for the constant of variation

To calculate the constant of variation (k) for a direct variation equation, you will need to determine the slope of the line. The slope is calculated by finding the difference in y-values and dividing by the difference in x-values. Once you have the slope, you can plug it into the equation y = kx, and solve for k. In this example, the slope would be (8-5)/(5-0) = 3/5. Therefore, k = 3/5 and the equation would be y = (3/5)x.

### Example calculation

In this example, we will calculate the constant of variation, k, for the direct variation equation y = kx through the points (5, 8) and (12, 48).

First, we’ll plug those values into the equation to solve for k:

8 = k(5)

48 = k(12)

Now we can solve for k by dividing each side by the matching x-value:

8/5 = k

48/12 = k

k = 1.6

## What does the constant of variation tell us?

In direct variation, the constant of variation is the slope of the line formed when graphing the linear equation. The constant of variation can be represented by the letter k. In the equation y = kx, k is the constant of variation. The constant of variation tells us how the dependent variable changes in relation to the independent variable. In the equation y = kx, if k = 2, then for every 1 unit increase in x, y will increase by 2 units.

### How to use the constant of variation to find the equation of a line

The constant of variation is a measure of how two variables are related. If two variables have a constant of variation, it means that their ratio is always the same. For example, if the ratio of two variables is always 2:1, then the constant of variation would be 2.

The constant of variation can be used to find the equation of a line when only two points on the line are known. The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. To find the equation of a line using the constant of variation, we first need to find the slope.

To find the slope, we take any two points on the line and calculate (y2-y1)/(x2-x1). For example, if we have the points (1,2) and (3,6), we would calculate (6-2)/(3-1) to get a slope of 4. Once we have the slope, we can use either of our points to plug into our y = mx + b equation to solve for b. For our example above, we would use (1,2) to get 2 = 4(1) + b, so b = -2. Therefore, our final equation would be y = 4x – 2.

## Summary

In mathematics, a function f is said to be directly proportional to a function g , if there exists a non-zero constant k such that

for all values of x where both f(x) and g(x) are defined. The constant of proportionality, k, is called the constant of variation and denoted as

The mathematics of this relationship are relatively simple. If you have two points (a,b) and (c,d) such that b=kc, then the slope between those two points is k. In other words, the ratio between any two corresponding values will always be equal to the constant of proportionality. You can use this relationship to solve for k when given any two points on the graph. For example, if you know that when , then you can solve for k by substituting those values into the equation and solving for k.