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Transcript
Model Direct Variation (4.6)
Definition: Direct Variation is a linear function that can be written in the form
y = kx (where x ≠ 0)
Definition: k is called the constant of variation
**Think of the y = mx + b form.
** y = kx means that m = ______ and b = ______
So all direct variations will go through the _______________________
Is the equation a direct variation? If it is, find the constant of variation (k).
** To determine if an equation is a direct variation, solve the equation for y.
Ex. y = 3x
Ex. y = -2x + 1
Ex. 5x + 2y = 0
Ex. 4y = 3x + 12
1
Graph the direct variation equation. (Graph like slope-intercept form, where k = m and b = 0)
Ex. y = -3x
Ex. y = x
Ex. 2x + y = 0
Ex. 6y = 10x
2
Solve y = kx, for k
To Write a Direct Variation Given one value for x and y
Step 1—Find k (Use the equation above)
Step 2—Write the equation y = kx and substitute your k value
Given that y varies directly with x, use the specified values to write a direct variation
equation that relates x and y
Ex. x = 2, y = -8
Ex. x = 40, y = 15
The graph of a direct variation equation is shown. Write the direct variation of the
equation. Then find the value of y, when x = 10
Ex
Find k (Use the point given)
• (3,4)
Write the equation ______________
Use the equation to find y
(substitute in x = 10)
3
Ex. The size of a file (s) varies directly with the amount of time (t) download a file. It takes 15
seconds to download a 420kb file.
a) Write a direct variation that relates s and t
b) How much time will it take to download a file that is 1260kb?
To determine if a chart is a direct variation, find k for each pair. If k is the same for each
pair, then the chart is a direct variation. If k is not the same, then it is not a direct variation.
Tell whether the table represents direct variation. If so, write the direct variation
equation
Ex.
x
y
0.5
9
3 -2 1
54 -36 18
Ex.
x
y
8
7
2 -4
28 7
-0.5
-112
4