What does it mean y varies directly with x?

direct variation
(Some textbooks describe direct variation by saying ” y varies directly as x “, ” y varies proportionally as x “, or ” y is directly proportional to x . “) This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

How do you determine if y varies directly with x in a graph?

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 = = 3. Thus, the equation describing this direct variation is y = 3x.

What makes a graph a direct variation?

A graph shows direct variation if it goes through the origin, (0,0) . The equation is y=kx , where k is a constant, which is apparent when we write the equation as yx=k . In slope-intercept form, the equation would be y=mx+b , where m=k , and b=0 .

What happens to Y if y varies inversely as x and x is doubled?

So, when x is doubled, y is quadrupled.

How do you know if something varies directly?

If something varies directly, then when one side of the equation increases, the other side increases as well. If you had 2 pitchers, you’d be able to fill 16 glasses. Thus, the glasses of lemonade that can be sold is directly proportional (or varies directly) with the number of pitchers of lemonade.

What does the K represent in Y KX?

So by the definition of slope, k is the slope of the line through these points. Thus, k is the slope of the line with equation y = kx.

How do you know if y varies inversely as x?

An inverse variation can be represented by the equation xy=k or y=kx . That is, y varies inversely as x if there is some nonzero constant k such that, xy=k or y=kx where x≠0,y≠0 .

What happens to Y if X is tripled?

y = c 1/x. Intuitively this means that if x doubles then y is reduced by 1/2 and if x triples then y is reduced by 1/3. For example if you are going on a 200 mile drive then the time it takes, y, is inversely proportional to your average speed, x. y = 200 1/x.

When do you Say Y varies inversely as X?

Since k is a positive value, as the values of x increase, the values of y decrease. Note: For direct variation equations, you say that y varies directly as x . For inverse variation equations, you say that y varies inversely as x . Product Rule for Inverse Variation

Which is the graph of the direct variation equation?

The graph of the direct variation equation is a straight line through the origin. Inverse variation describes another kind of relationship. We say y varies inversely with x (or as x , in some textbooks) if : for some constant k . This means that as x increases, y decreases and as x decreases, y increases.

When does the ratio of Y and X vary?

We say y varies directly with x (or as x, in some textbooks) if: y = k x for some constant k. This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

When to use Y as a direct variation?

Suppose y varies directly as x, and y = 20 when x = 4. Find y when x = 9. When we see the phrase “y varied directly as x” that tells us when should be using the equation . The next piece of information tells use that y = 20 and x = 4. We will use this information to find the value of k.