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 . (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.
The graph of the direct variation equation is a straight line through the origin.
Step-by-step explanation:
Example 1:
Given that y varies directly as x , with a constant of variation k=13 , find y when x=12 .
Write the direct variation equation.
y=13x
Substitute the given x value.
y=13⋅12y=4
Example 2:
Given that y varies directly as x , find the constant of variation if y=24 and x=3 .
Write the direct variation equation.
y=kx
Substitute the given x and y values, and solve for k .
24=k⋅3 k=8
Example 3:
Suppose y varies directly as x , and y=30 when x=6 . What is the value of y when x=100 ?
Write the direct variation equation.
y=kx
Substitute the given x and y values, and solve for k .
30=k⋅6 k=5
The equation is y=5x . Now substitute x=100 and find y .
Answers & Comments
Answer:
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Step-by-step explanation:
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Answer:
DIRECT VARIATION
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 . (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.
The graph of the direct variation equation is a straight line through the origin.
Step-by-step explanation:
Example 1:
Given that y varies directly as x , with a constant of variation k=13 , find y when x=12 .
Write the direct variation equation.
y=13x
Substitute the given x value.
y=13⋅12y=4
Example 2:
Given that y varies directly as x , find the constant of variation if y=24 and x=3 .
Write the direct variation equation.
y=kx
Substitute the given x and y values, and solve for k .
24=k⋅3 k=8
Example 3:
Suppose y varies directly as x , and y=30 when x=6 . What is the value of y when x=100 ?
Write the direct variation equation.
y=kx
Substitute the given x and y values, and solve for k .
30=k⋅6 k=5
The equation is y=5x . Now substitute x=100 and find y .
y=5⋅100y=500