7.3 Direct Variation

In the formula, y=kx, k is referred to as the constant of variation OR the constant of proportionality. It is the coefficient of x (not y!)

A constant does not change in value.

• The line on a graph will ALWAYS pass through the origin!

• Nothing is added or subtracted from kx in the formula; there is no "b". It is simply y = kx (y = mx would also work)

• All ordered pairs are proportional. If you divide the y from one ordered pair by its x and do that for all ordered pairs, the ratios will be equal!

Step 1. Plot a point on the origin, (0,0).

Step 2. Use k like you would slope to plot two more points.

Step 3. Connect the points with a line (with arrows on each end!)

This video is less than two minutes in length and shows one way of solving "varies directly with x" problems. ("directly proportional problems are done the same way)

Remember that y = kx is the same as y = ax.

For each ordered pair given, (-4,1),(-3,0.75). (-2. 0.5) and (-1,0.25) if you divide the y value by the x value you find k for the ordered pairs. IF k is the same for each, then you have a direct variation and have found the constant of variation/the constant of proportionality

Direct variation describes a simple relationship between two variables . We say y varies directly with x if: y=kx. for some constant k , called the constant of variation or constant of proportionality .

The Graph of a Direct Variation will graph a straight line that will pass through the origin. The slope can be positive or negative. The slope of the line will equal the constant of variation.

Using Tables

You can solve problems involving direct variation. Just Remember

y/x = y/x..

Using Tables

• Direct variation describes a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if: y=kx. for some constant k , called the constant of variation or constant of proportionality 

• The number of hours you work DIRECTLY impacts the amount of money you make

• The amount of weight on a spring DIRECTLY impacts the distance the spring will stretch

• The speed of a car DIRECTLY impacts the distance traveled in a certain amount of time.