About Direct Variation When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation.
I always start with the "shower problem". We then mentioned that boys usually don't want all that fuss I let several kids share I then make a table label one column time x and other column gallons of water used y.
We then complete our table We then take this information and graph it on a coordinate plane using time as the "x" and gallons as the "y" value This makes sense to students as it is all based on easily understood data. I like to present all of this information in one lesson and connect the meaning to the table, to the graph.
We then brain storm other examples of what could be called "direct variaitons". After we have generated several real life examples and table of values which match these scenarios, we try to come up with an equation which fits this information. Allow students several minutes to discuss this with a partner or group to generate an equation for each scenario.
Teacher may need to help to guide this to happen depending on abiility of the class.
Depending on a students background, I write this lesson as a follow up to linear equations, we can discuss how the "k" is really acting as the slope.
This is always how "k" is defined, but rather than throw all these definitions at students, allow this value to logically follow from the previous discussion and in that way connect this idea to prior knowledge.
We now can discuss that a direct variation is simply a linear equation, with "k" playing the role of "m" slope and always having a y-intercept of 0.
The above takes approx 30 mins Next use the power point attached here to investigate several table of values to determine if they represent a direct variation. Get students to share their thinking What was the first point they looked for? What is they saw the point 0, 0?
Would this give them any information?Substitute your coordinate into the direct variation equation to solve for the constant of proportionality.
Relationship: k = 2 y = 2x A direct variation equation can be represented by a proportion: A direct proportion can represent 2 different coordinates (,) and (,). Graphing Linear Equations in Slope-Intercept Form; Writing Linear Equations in Point-Slope Form; Graphing Linear Equations in Point-Slope Form; Standard Form of a Line; Graphing Linear Equations in Standard Form; Determining the Equations of Horizontal and Vertical Lines; Graphing Horizontal and Vertical Lines; Determining the Equation of a.
relationships, and how to write equations that express direct variation. Students explore a context in which a regulating line is used to estimate the dimensions of similar rectangles. Students are given tables of data and asked to determine if one variable is directly proportional to the other variable.
They also write equations that model. This lesson explains some examples of direct variation, how to write direct variation equations from the scenarios, and finally, how to solve a direct variation problem.
The concepts in this lesson are explained very well. Direct Variation Worksheet Is each equation a direct variation? If it is, find the constant of direct variation. Are the following graphs examples of direct variation? If yes find the equation, explain if not.
Write an equation for the relationship between weight and mass. b. If another object has a mass of 8 kg, what would.
Find the Intercepts of the Graph of an Equation x-intercept The x-coordinate of the point where a graph intersects the x-axis. Write the direct variation equation that passes through the given point. Then ﬁ nd the value of y for the given x. (2, 25); x 5 20 (23, 29); x 5 43